{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":52050,"title":"Matrix convolution","description":"A certain convolution step involves an elementwise multipication between two 3x3 matrices and taking the resulting sum of the elements.\r\nGiven a 3x3 kernel matrix K, find its convolution with a 3x3 subsection of a given matrix A. The subsection will be indicated by r and c, the row-column location of the top left corner element.\r\n\r\nFor example, let K = [  ], A = [   ] and r = 2, c = 3. Then the relevant 3x3 subsection of A starts at row 2 and column 3, i.e. with the element 7. Thus, the 3x3 subsection is S = [  ]. The element-wise product of S with the kernel K is [  ], and the convolution y is the sum of these elements, making y = 45.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 354px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 177px; transform-origin: 407px 177px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA certain convolution step involves an elementwise multipication between two 3x3 matrices and taking the resulting sum of the elements.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.5px 8px; transform-origin: 81.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a 3x3 kernel matrix \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5px 8px; transform-origin: 5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eK\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 187px 8px; transform-origin: 187px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find its convolution with a 3x3 subsection of a given matrix \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 106px 8px; transform-origin: 106px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The subsection will be indicated by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3px 8px; transform-origin: 3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 173.5px 8px; transform-origin: 173.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the row-column location of the top left corner element.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 222px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 111px; text-align: left; transform-origin: 384px 111px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.5px 8px; transform-origin: 52.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, let \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5px 8px; transform-origin: 5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eK\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = [ \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-24px\"\u003e\u003cimg 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style=\"width: 85.5px; height: 60px;\" width=\"85.5\" height=\"60\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ], \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = [ \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-45px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAO4AAADMCAYAAAB0ip8fAAAUN0lEQVR4nO2dXZXrOgyFN4cyCIESGARFUAbDoAxKoRgKoRxKoRiGwrkP6b5R3Dhx4t/M7G8tP5w5SSM7ki3LjgUIIYQQQgghhBBCCCGEEK3SATgsXHME8BVYjtkk7Un1nMP7d5bq3hoh76s1rP7Ukn1tu83p/O39e1Xo3gL8w7IRvN7XhZRrBlkPRlZbfgB8b/zNJ8Lq3gpr3lcLUN4fAJd34b8fKKf4W9rtgF5On44/0osZJpRrBHMVOiHcaP+h75FS0mG+Ebd0FheE1b0F1r6vFjhiMFB3lOP//SCv8ca0m9WPEjq+yOkt1AnDiLNUoQeWe8jD+3deacT8eP4LwNn87YjPl3IK/L0v7McItryvFqCH5nsn3+//v2V6fky7cbTd6sllJ2TU6dC/hKW5wRl53OQT+kb0yWfrcA/4Pb6UO/ZjBGQvXsIRy3Ky8/wpIM/advtGfm8gilDDDXELaAipXYg75ns+jvShSnBHP4LbUbdlI7DsxXBt2/pGXF6Tw0NzWdtuL/SjdLOBy1SKQOP5QfqKhkTvHggz3G/0L4Wd0R6MwLIXw7Wd6RPTOnFFvkCmy5p2O5trbR3OaMiIUykCK5trvrIEDXcu0seACD0CGW5ebPzBDVDxXbATzc2adptbPbH6U5VUikA3OTQ4lBo29pxL/cS4d5fh5uWAcVCISs+YxQ3lRrC17UY5r5g25Fp6/j8pFCGnmxxCh2Gu5Ou9r/h02WS4+XGNl3pSWvFj2+2M8XJkLV3/nxSKUNtNZh18o+0XpqPSMtwy+Iy3pPypBihbj0sa0baRokI13WQu7fjmtnPrcTLcMlDmKz430ZTSmVTtZjcCVdk5RWIrVNtNvsMfteT/+9Z2Zbj5YYCKBtphCCSylAj2pGw31qnE+rOXFL5/LTeZSzs+ubmIfsL0JnHu3PmHvh61N8CHsCfDpaxTHaeNOLe4jjsHt//u2nDZe5Z2k8+YN1rgs2cPLS0bxJ4Mly6lTzfszrXco27Kdiu5ccRLTIUYzS3tJocYLdDPqR4zxQYangjbj12bvRhuyDTEbovMvSc4x4hbKxgLIK5CuTeJT3HCstEeEWZ8muPmI7Rt92i47ry9CjEV4oh1XrowEe7OpykYspfh1oeusk8/7LbI3F5OaLvxYAWfPPQyq0aUge2KYN3kEq4ljfaJ4YPsqfJCeKPKcPNCWX1Rf3psIV90pZJlqd3sctUFY7k5KDwXfiM7/Fxvy4IyG71Ez0OjDQ0ubfkmt3UjAOLeVy34IYGr7Iz435E/PrKm3dyA5ut9PdegS27T/KCDP3BzQ9h8g/eX8PP5GV5IWaMIR+wjIJXifdWkQ6/8Vu4L8keSt7bbGWOdu73lbVlHhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCtAATXW05nvSI+cOjW4VyT5Ub2qvPnLxuKXXMbIe4Y0p58Hjpo05j5T6iP/Hx9i5FsxkcMM6WxuLLIzt1r3vO8Qtl0iXGwny5vjOZq59QP4E9E3ipXDPL0mHQnZhOglkwSnY0W+U+YDhsn+cyF+/cbWLetS+fJ7n/vK+5YJxxrUTWtVjsifZTpTX5mWAqtOSSf6qz32p0JbMxxMp9xGCwVc/ffrwFsflcjvis3JQLwMOhXVfDZhpoccQic9npWyXkwHbm4MmV9vGE3thOGGc43GJ0NntEbsONlZu5nzmYVctgcEKvuD7BbU/o5nP5mvibpYks3Qsw7UVrc1gfTJ2xpDBUsNxuMhA3WrLjtF5aKVd5rdy2g3mgcrLzO+ZHG5s9zTXAE+YV3iZ4apUXevlazzpPOoS5vjSEEm5+jOEyrUeNnE1r5LZxkCY6+pCIKZMerR05OeK26oZat4fl+f77HozYBzvbUsnFtxruN/qOk51Ry4Zrp40lvJgk0HDXzFXZQ1V3KWaYi8wu5dxtGXZIpZKLbzFcN69xy4Zrvc5/GAa65pc+qeChIycjzSXSJcbyhd7lv2LakKtmGN8I3eRSsm8x3CfGI1fLhvttrmOKzamlz6Y8SyarpkszxwF9b28r1Xq6ShdX/lLuZipKu8nAesO94jOxdcuG6y5vcpPFF3p9sR1+M240K7fUmzDC7CYBbmYyvwJ6DJR/D8miSWk3GVhnuF+YXsVo2XCtLkzZgasv1b00O09diztyzS0btYjdlNLyOrRLaTcZWDdX9K2Zt2y4IQOQ3RRTXV/u+HRp1mCVf28uJ7CPdWhLDTcZWOdy+jrwvRjuHE1Mrxiqj23EK8q/kFSwF92L4dZwk4EwA+BGF84N3WIDQGfz95wGEGq4dvCZw04Tq+g6J9wpHl6jJ00FZc+1bTA1VJzSc6wQA5iKfYSUnDoTarh2H8NcR1LVcFMaLTAo/15GLQtH3NIj2BYY/a/hpoUYwBXDHuupYoM7T4Ttxy4hNxDuNYYaeHJOWDbaI9Y1Zsk9s6nhHLd6lDAAupo1OpkUX/a0PMc9muvOM9dxWajoFl93J8sUDHuvMVx+edSam8yPtn114QhWPUIYCEesOcXKxW83XGBoX59R2t1Vxd4BjfaJvjK+8sJYkelC+D6Yb3nEsktVF4xdG3ZQT7TX4Uxh3eQa6+V/wXCtfFOGyd8q1tHb72ZDijVC93vdBwYj55bHVhXfDZZwK9sVfXtMfWPcKnSTa3gH/MzQdoJbKG24W+S2exPshyhs/6JbfLnbKaS4gh3eQttrru+/7WGn1Bnj+t9Q6QiSSBj4KenZdPAHnG5Yv2/3iDIBqVi5qfNWby7Y7wcpQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQggh9gQPHt/LUaeWI/oT/G4YkhmXoMP69jpi/oD3nDBB15ZjVTtzf2li5I65dxfwBPi9VPCA4fB3nrdbyhg6DGdVh7TX4X29ey6274D6lPDZ7rnbvvy3LsxRdcfQOfLenJ18jNyxdd4NKU64L8kRg8HmPt/XMqUQS+3FbAs/6M8JvmBIas2Sy3ht3mNfmcsVdfNcYw92z2G8MXLH1nk32JPp92C4TE7GF1DKtT+hN7oTxhnrltqLB3i7ctrMFLkyGzAflE3FccRn5zM1taBxvjDdxswwkcMIYuSOuXc3HNArjx0BWjZc28nk6u1DCPVQvuDP7A4MypQjtenp/bs++WwdXBmpF3OGaTvQlDoTI3fMvbuC6Rn2kNTaKlOtpFkk1HBPmJeTv5Mj3eMd8/M5m7XO7Ths1nnfyNSZa1KOujFyx9y7G77RuxSMFrZuuNbVqT1HSRUTYJ1yBExuWO7cbIJni50KzP0GO9LXRhmniJE75t5d4ObYbd1wbU9planW0koKw6UHUdPlpxK7c+zQUclmUiz5Dnxy5763Ok+MR63WDde6bkyzObW0UirUH2u4jDQXTfc4ASPztt1sVvc1hlsy2DMld4l7q3JFrzRWYVo3XHf5hJssvjCsM5Z0o7ca7gHj3K3s+WvM1zlH5XSJWF1YY7ilDMEnd+57q/KF6ahb64Zr51xTCnJwrsnd+28xXEaY3UTdtYJtrIPbnlYXliKvth1KeztbnhdzbzU4p5oSunXDDVHwE8ajWE5SzHHdkbfk8oSdX7u4S25zXFHWcOfkznlvVe7wK8eeDDf0upxzx1RRZbvLJ7fMljs+p0ukZVd5Tu6c91bjG/1L4LzQLTb4czZ/b6WSVrnnsIqUswNKuUXUjlolOk0uA849a4vh5pY9RO4c91Zlal4VUlqpqF17m+tM9mi4Jb0dBvKWnsNgX6jh5p6jh8qd+t7qXNE3sq/YwM7T/L2VyFvoqBRq4LHkMNzcGwLWKLDd7BIyMufY+UX+rNGG0Poc164tnmeu40iRU5GAtIbLPb85l7FOWFbgI4aO2uqDr73tO8k1v10rd6p7d0PrhgsMXoHPKO3uqjnjTkFKw+XXLLna3d0lNwWX06wSL+0wohfk+3oolq1yx967K/ZguEujAI2pRLg/1HCtck8pEV3SXOvOVOAnepl95YXPdrMRb7eO9oOPHN8Sx8gdc+/u2IPhAuO1zzOGnp5R8RJbCDuMd2pdZq51vwF9YFAcbnnMPdKGBiKnOg/+ht2002HwfnJ0ODFyp6jzrjiivYCUjwN6Q+UuJBpD7iNgOviDfDf4d3R9O9de33/L3c62fZbKXIfntjc/ncslf4zcqeoshBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBDiL9Nh/Yl1HYbkXrXYIjdlrnmM7N7kTvHsLXWuzRF9vZs7ubTDcHZv6EthPpU7+mNNbxjy5pZ6MWvlPuDzjGLm2ymZpHiL3Ff07W0P4n4hv9yp2myLjtWE9XbPV/YdSl+UqZeyJpmTm6eGB4o/kNd4t8htT9T3lZx5d4Dtcj8xnaLjjrztnaLNtupYTZhW5Ad9/S4Y2pqlmvGe3gKdMM6yt9SoNE5frhfmisllBFvlZm4dm3bkiE+lynUq/Va5ee1UpgObwmMuE8JWYttsa51rw8PpXf22GQ6aSDsSmsPGKorPMJk1rsQLCpX7hHH6i7nfuacUMOB5c3KHtKU1opSjbuo2S5ngLCdfmK8P2zt3OtMgQhvVZpz39bKduSa36xkqN9Nd+LAZ+kq8kDVyL8lkjTvlqJu6zfZiuCfMB6FYj9wpWIMIbVTr7sxVjqPyK5WAHkLlvmE5ImiTWecmVG6245xMNtFaSm8hdZvtxXCX4IhbMpjpJbRRQ3vYB8IMPJbU+WVLzV1StncXeF0O1rTZbzBcThVzB1+DCWlUmzl8jeHmTEGYUhmY8rJET7rWcJfmr7UMd02b7d1wGWluKjtfSKNal2yN4eY0hFTKwFHrhTKL7KFyh3aANQx3bZvt1XAPGOdTpofRxGaMtYa7NJeyv7cHw+XvlJq3bAkG+tq8lqu8ts32aLiMMNsO1LZ1deNda7hLc5or9mO4dt5SijXLbzZr/dSoa5eDSkU6t7TZHg3XxR15SywdzvKXXeU7eoUvOW9ZI/cRY+N9vO+/on8PdkfPLZO8Llva7DcYLjDeTfaDyvPdnFHlnC8pVhm+0RtFaUVaKzfnWTf0bcv94R3G3k3OQCDZ2ma/xXCBcZtXrUtoo7LnDzXc3POAGGXgRxI1Gj6VEtudbL4tqCmJabPfZLjW+9yF4d4Crys159qqDDWNFkgfVPuH8X7iHMS22W803OrbHkMb1fY0PkWx6725o7RblOGEZQU8ol1Pgdh2zh0kSdFmv8lwuc0095beRdY06tJuGfr/JVy3tcrArzvmPsniQnvLhmujzbl38aRqs99kuPxqqno91jSqjaq519o5V4nvFddGZ3/QK9hlpryQf2koRoltlDn3Lp6UbbYXw7UDz5QOc7pYIhA4S4fxckPIFyZ8ofazL37wXapSa+S231GGlJzyb2lvcsHQ7rmnISnbLKbOpXG/Neby2wXDlseqHQ+XEh4T5YZlxTi8r+HOEn4Glns3yRa5757rp0quUWyL3Af0BsE12wfKHQ2Uos1idawG1Gsr6xVldFv8Ejr0CvOFhja2CyGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCHK02H7oWQx98ay5dlH9Iew1TiIjc/dcqbyl6fc0P4phFvr3QJNyt5hOE92rWAx98ay9tm8/gfDWbn8d+4s4wd8ntnL/DMhx5Taw+anSsn8vmuIrXdNDuiPZn1hfPj7C5Vln2rUUOOLuTeWLc/mAd9TKTvsAe85jNdmf/CVpTw0NhPAVCmROWItKepdCx7wP5VKhzmJc6d/meSEXhlOGDIQhBpfzL2xbH02T9L3nbj//f7/HMmhmWvGJko74rPz8cnG0bb1Ecoltt41oW5NZV2w3k/VrAwxeV1q5oQJffYx4LpcqRNPGKdqcbF18GXd+0b+XMOpSVHvWjAb35y+2M6n2mH1v91wbXpQX+/Oa14pBcSQmsXHAeN53xQv9CPAnjIapKh3LegKz8lljbvaqPvbDdcqyRPTys8sbannXCHRXqYunVIUqyC2Dme0bcSx9a4J3eA5uexgUM1j+O2GC4xdGzeowODUC3Xc0bmcwzbL3VRktsWgVChLuZZrEeIJdIHXZeUvGC6TL7tKz7nYDfVGMBqnz7WknFdMG3KLwZ0QlupdC9u2czohw93I2me7xstGr6n47LnXjPZnjJdZftC22zzFlnqXgp7AUqcow93Ilmf7jLfWjhjWYe2o49aj5WTRU2ytdwm4NDg3f5WrHMGWZ/MeJouu6XJyPXDrHM9ucGhtnjhHbL1zc8B4SjKlFzZm8iwn2pi/YrhsbL6IDmO36B/KBnvu8Ee5Q2GdWovMzpGi3rk5Ymy8D/T6xg7/bv4vx6adIP6C4fLaKdfH9p6p13F9fL+fFdtmJ+zLcFPVuwQH9PGEG3rDvaPXow7D8mHV4OBfMFy6lL5Gtj1o7lH3jHTKm2vjSA5S1rsmdsvj1F7mYvx2w/0KuM5ui8wZMEmtvBxxq7lrgfwWowXGendeuLaYIH/VcIH8hnvCsvIesW55xJ23t0iOetfCdvDV91j/dsMFBtfG10PabZE5FIi7s+bccC7xdObfXzPycEmi1egssK3erWKjzVU+6XP5C4bLa33RTK7d5ehFqbxPDB9kT5UXxkZol6sujtxU9ifadT+31rtFbJT5jgaMtsM47L1mIT/m3li2PJuRQFfZ+dlcjhdC5f0XWKzL6y5V8SQGLknU3Ka5REy9W+OC4aCF6htGGNJ+TJQb5gWMuTeW2Gd36F+Eve+CfJHku0fWqTLVcZyd37hhWJJomdh61+SAYW84N4p8oy0ZhRAOHXpD3dP3z0IIIYQQQgghhBBCCCGEEEIIIWb4D842LQjIDGP/AAAAAElFTkSuQmCC\" style=\"width: 119px; height: 102px;\" width=\"119\" height=\"102\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22px 8px; transform-origin: 22px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  ] and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3px 8px; transform-origin: 3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 2, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 137.5px 8px; transform-origin: 137.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 3. Then the relevant 3x3 subsection of A starts at row 2 and column 3, i.e. with the element 7. Thus, the 3x3 subsection is S = [ \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-24px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 64.5px; height: 60px;\" width=\"64.5\" height=\"60\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.5px 8px; transform-origin: 65.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ]. The element-wise product of S with the kernel K is [ \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-24px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 115.5px; height: 60px;\" width=\"115.5\" height=\"60\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 217.5px 8px; transform-origin: 217.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ], and the convolution y is the sum of these elements, making y = 45.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(K,A,r,c) %Do not alter this line\r\n  y = 1;\r\nend %Do not alter this line","test_suite":"%%\r\nA = magic(5); K = [-1 -1 -1; -1 8 -1; -1 -1 -1]; r = 2, c = 3;\r\ny_correct = 45;\r\nassert(isequal(your_fcn_name(K,A,r,c),y_correct))\r\n%%\r\nA = magic(5); K = [0 -1 0; -1 5 -1; 0 -1 0]; r = 1, c = 2;\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(K,A,r,c),y_correct))\r\n%%\r\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'for')),'loop forbidden')\r\nassert(isempty(strfind(filetext, 'while')),'loop forbidden')","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":428668,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-06T14:45:47.000Z","updated_at":"2026-03-30T17:19:23.000Z","published_at":"2021-06-06T14:45:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA certain convolution step involves an elementwise multipication between two 3x3 matrices and taking the resulting sum of the elements.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a 3x3 kernel matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find its convolution with a 3x3 subsection of a given matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The subsection will be indicated by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the row-column location of the top left corner element.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, let \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = [ \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-1 \\\\;\\\\; -1 \\\\;\\\\; -1 \\\\\\\\\\n-1 \\\\;\\\\;\\\\;\\\\;\\\\;\\\\; 8 \\\\;\\\\; -1 \\\\\\\\\\n-1 \\\\;\\\\; -1 \\\\;\\\\; -1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e ], \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = [ \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\;\\\\; 17\\\\;\\\\; 24\\\\;\\\\;\\\\;\\\\;1\\\\;\\\\;\\\\;\\\\;8\\\\;\\\\; 15\\\\\\\\\\n\\\\;\\\\; 23\\\\;\\\\;\\\\;\\\\;5\\\\;\\\\;\\\\;\\\\;7\\\\;\\\\; 14\\\\;\\\\; 16\\\\\\\\\\n\\\\;\\\\;\\\\;\\\\;4\\\\;\\\\;\\\\;\\\\;6\\\\;\\\\; 13\\\\;\\\\; 20\\\\;\\\\; 22\\\\\\\\\\n\\\\;\\\\; 10\\\\;\\\\; 12\\\\;\\\\; 19\\\\;\\\\; 21\\\\;\\\\;\\\\;\\\\;3\\\\\\\\\\n\\\\;\\\\; 11\\\\;\\\\; 18\\\\;\\\\; 25\\\\;\\\\;\\\\;\\\\;2\\\\;\\\\;\\\\;\\\\;9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e  ] and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 2, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 3. Then the relevant 3x3 subsection of A starts at row 2 and column 3, i.e. with the element 7. Thus, the 3x3 subsection is S = [ \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e \\\\;\\\\;7\\\\;\\\\; 14\\\\;\\\\; 16\\\\\\\\\\n13\\\\;\\\\; 20\\\\;\\\\; 22\\\\\\\\\\n19\\\\;\\\\; 21\\\\;\\\\;\\\\;\\\\;3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e ]. The element-wise product of S with the kernel K is [ \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e \\\\;-7\\\\;\\\\;\\\\; -14\\\\;\\\\; -16\\\\\\\\\\n-13\\\\;\\\\;\\\\;\\\\;\\\\;\\\\; 160\\\\;\\\\; -22\\\\\\\\\\n-19\\\\;\\\\;\\\\;\\\\; -21\\\\;\\\\;\\\\;-3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e ], and the convolution y is the sum of these elements, making y = 45.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":52050,"title":"Matrix convolution","description":"A certain convolution step involves an elementwise multipication between two 3x3 matrices and taking the resulting sum of the elements.\r\nGiven a 3x3 kernel matrix K, find its convolution with a 3x3 subsection of a given matrix A. The subsection will be indicated by r and c, the row-column location of the top left corner element.\r\n\r\nFor example, let K = [  ], A = [   ] and r = 2, c = 3. Then the relevant 3x3 subsection of A starts at row 2 and column 3, i.e. with the element 7. Thus, the 3x3 subsection is S = [  ]. The element-wise product of S with the kernel K is [  ], and the convolution y is the sum of these elements, making y = 45.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 354px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 177px; transform-origin: 407px 177px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA certain convolution step involves an elementwise multipication between two 3x3 matrices and taking the resulting sum of the elements.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.5px 8px; transform-origin: 81.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a 3x3 kernel matrix \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5px 8px; transform-origin: 5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eK\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 187px 8px; transform-origin: 187px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find its convolution with a 3x3 subsection of a given matrix \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 106px 8px; transform-origin: 106px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The subsection will be indicated by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3px 8px; transform-origin: 3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 173.5px 8px; transform-origin: 173.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the row-column location of the top left corner element.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 222px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 111px; text-align: left; transform-origin: 384px 111px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.5px 8px; transform-origin: 52.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, let \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5px 8px; transform-origin: 5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eK\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = [ \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-24px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKsAAAB4CAYAAACNQgKYAAADyklEQVR4nO3d0XHiQBCE4c5BGZCAEiACR0AGZKAMSIEYHIJzcAqOgRR8D+stCQrp7Fqx2tb8XxVP5ypGM20fSKCRAAAAAAAAauu3LqAB0XvQSTpsXcSSk6QvSe9bF7Kh6D3oJA2SbpLOG9fy1JvSgL5/HhEHRQ/GkOYeNBfWi1JRZ8UdVPQeHJR6cJJ0VcNhnYo4qEfRe3AUYbURvQeE1Uj0HhBWI9F7QFiNRO8BYTUSvQeE1Uj0HqwS1uMKj/9pYVC9yo+zK3j+FnpQY9ZLz10c1u/Cx+0Pz7HloD5Ufqwl1/Vb6EGNWc9ZJawfhY/fNL+FQV1UfqwlH8BooQc1Zj2H16xGoveAsBqJ3gPCaiR6Dwirkeg9IKxGovfAIqyDxiK/1PhXGl4keg86pV/S6S9syTnr1Z2Uinp2CmRQjO8i0YN0nHOnwQY1FloAAAAAAAAAAAAAAAAAAAAAAAAAALAzEb7NOdVpvFVktGN/xqIH0bbrTY93+Hl8quHtei9mMf+I2/XycrK3hX+7VK1oOzbzj7hd76R0nJ8LP5PXQu79riy287cqtkC+Rc7SceY7cEd6OWA1f6tiC+QgLv1lzT9zqlJRG6zmb1VsgYvGY30Wxk7jvfn3/jJgymr+VsUWOOh+YcTjm6z8BmuoXNfWrOZvVWyh/CYrP65KIX5Xemf87CzB3lnN36rYFTwGtsl7klZkNX+rYlfyLLAXxQzsavOPsmGwpl7pjEC+ce40sB+qH9jdbFcs2TiX39lWK9ZAr9STaSjPGi8G5MDWtJvtilE2DNbQaQzl43B73Qe25nlWtiv+gVWxBfKlxbmLAr22++u6Jav5WxVbIP93u3Sc+ZJsydJeN1bztyq2wG/CmtcMEdZGWRVbIL8M+Fr4mXxJ9lqlojZYzd+q2ALTN1hznw3In++0+NT8SmzmH227Xq8xkGeNp68OSi8Tbop1ydVi/tG3652U/qvPx3zVfXj3Lvr8AQAAAAAAAAAAAAAAAAAAAAAAAABAC/hGIz3o1OjXsTOLDXMvFr0HndJXsJvdsmizYe6F6MEY0tyD5sJqu2FuRdF7cFDqQb7hR7NhnYo4qEfRe3AUYbURvQeE1Uj0HhBWI9F7QFiNRO8BYTUSvQeE1Uj0HqwS1igbBnezZa9AjVkvPXdxWEs3z7lsGNzNlr0VanjlrOesEtYoGwbZsldn1nN4zWokeg8Iq5HoPSCsRqL3gLAaid4Dwmokeg8swmqxYe7Foveg07gNPP/CNrW8jg1z9EBKxzl3GmxQY6EFAAAAAAAAAACV/QMvtDv3jUSzkwAAAABJRU5ErkJggg==\" style=\"width: 85.5px; height: 60px;\" width=\"85.5\" height=\"60\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ], \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = [ \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-45px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 119px; height: 102px;\" width=\"119\" height=\"102\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22px 8px; transform-origin: 22px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  ] and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3px 8px; transform-origin: 3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 2, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 137.5px 8px; transform-origin: 137.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 3. Then the relevant 3x3 subsection of A starts at row 2 and column 3, i.e. with the element 7. Thus, the 3x3 subsection is S = [ \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-24px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 64.5px; height: 60px;\" width=\"64.5\" height=\"60\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.5px 8px; transform-origin: 65.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ]. The element-wise product of S with the kernel K is [ \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-24px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 115.5px; height: 60px;\" width=\"115.5\" height=\"60\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 217.5px 8px; transform-origin: 217.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ], and the convolution y is the sum of these elements, making y = 45.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(K,A,r,c) %Do not alter this line\r\n  y = 1;\r\nend %Do not alter this line","test_suite":"%%\r\nA = magic(5); K = [-1 -1 -1; -1 8 -1; -1 -1 -1]; r = 2, c = 3;\r\ny_correct = 45;\r\nassert(isequal(your_fcn_name(K,A,r,c),y_correct))\r\n%%\r\nA = magic(5); K = [0 -1 0; -1 5 -1; 0 -1 0]; r = 1, c = 2;\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(K,A,r,c),y_correct))\r\n%%\r\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'for')),'loop forbidden')\r\nassert(isempty(strfind(filetext, 'while')),'loop forbidden')","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":428668,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-06T14:45:47.000Z","updated_at":"2026-03-30T17:19:23.000Z","published_at":"2021-06-06T14:45:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA certain convolution step involves an elementwise multipication between two 3x3 matrices and taking the resulting sum of the elements.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a 3x3 kernel matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find its convolution with a 3x3 subsection of a given matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The subsection will be indicated by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the row-column location of the top left corner element.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, let \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = [ \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-1 \\\\;\\\\; -1 \\\\;\\\\; -1 \\\\\\\\\\n-1 \\\\;\\\\;\\\\;\\\\;\\\\;\\\\; 8 \\\\;\\\\; -1 \\\\\\\\\\n-1 \\\\;\\\\; -1 \\\\;\\\\; -1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e ], \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = [ \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\;\\\\; 17\\\\;\\\\; 24\\\\;\\\\;\\\\;\\\\;1\\\\;\\\\;\\\\;\\\\;8\\\\;\\\\; 15\\\\\\\\\\n\\\\;\\\\; 23\\\\;\\\\;\\\\;\\\\;5\\\\;\\\\;\\\\;\\\\;7\\\\;\\\\; 14\\\\;\\\\; 16\\\\\\\\\\n\\\\;\\\\;\\\\;\\\\;4\\\\;\\\\;\\\\;\\\\;6\\\\;\\\\; 13\\\\;\\\\; 20\\\\;\\\\; 22\\\\\\\\\\n\\\\;\\\\; 10\\\\;\\\\; 12\\\\;\\\\; 19\\\\;\\\\; 21\\\\;\\\\;\\\\;\\\\;3\\\\\\\\\\n\\\\;\\\\; 11\\\\;\\\\; 18\\\\;\\\\; 25\\\\;\\\\;\\\\;\\\\;2\\\\;\\\\;\\\\;\\\\;9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e  ] and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 2, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 3. Then the relevant 3x3 subsection of A starts at row 2 and column 3, i.e. with the element 7. Thus, the 3x3 subsection is S = [ \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e \\\\;\\\\;7\\\\;\\\\; 14\\\\;\\\\; 16\\\\\\\\\\n13\\\\;\\\\; 20\\\\;\\\\; 22\\\\\\\\\\n19\\\\;\\\\; 21\\\\;\\\\;\\\\;\\\\;3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e ]. The element-wise product of S with the kernel K is [ \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e \\\\;-7\\\\;\\\\;\\\\; -14\\\\;\\\\; -16\\\\\\\\\\n-13\\\\;\\\\;\\\\;\\\\;\\\\;\\\\; 160\\\\;\\\\; -22\\\\\\\\\\n-19\\\\;\\\\;\\\\;\\\\; -21\\\\;\\\\;\\\\;-3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e ], and the convolution y is the sum of these elements, making y = 45.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"elementwise 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