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MATRICES with customized sum for rows and columns

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I want to create 4 matrices (6x10) with sums of rows and columns as following; in a single program/code.
mat1: sum_row1=sum_row2=......=sum_row6=r(say) sum_col1=sum_col2=......=sum_col6=c(say)&&&&&&& r=c
mat2: sum_row1=sum_row2=......=sum_row sum_col1≠sum_col2≠......≠sum_col6
mat3: sum_row1≠sum_row2≠......≠sum_row6 sum_col1=sum_col2=......=sum_col6
mat4: sum_row1≠sum_row2≠......≠sum_row6 sum_col1≠sum_col2≠......≠sum_col6
Kindly suggest some logic/program
Thanks

Accepted Answer

Michael Haderlein
Michael Haderlein on 7 May 2015
Edited: Michael Haderlein on 7 May 2015
To get mat1, you can use the magic function:
>> mat1=magic(4)
mat1 =
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
>> sum(mat1,1)
ans =
34 34 34 34
>> sum(mat1,2)
ans =
34
34
34
34
mat2, mat3 and mat4 are easy, for instance use randoms and normalize the columns/rows:
>> matrand=rand(4);
>> mat2=bsxfun(@rdivide,matrand,sum(matrand));
>> sum(mat2)
ans =
1 1 1 1
>> mat3=bsxfun(@rdivide,matrand,sum(matrand,2));
>> sum(mat3,2)
ans =
1.0000
1.0000
1.0000
1.0000
mat4=matrand;
  3 Comments
Michael Haderlein
Michael Haderlein on 7 May 2015
Edited: Michael Haderlein on 7 May 2015
Oh, sorry, I didn't read that you need 6x10 matrices. However I'm confident that in this case mat1 only exists if all the sums are zero. If this is fine with you, create the matrix with
>> matrand=randi(100,5,9);
>> mat1=[matrand -sum(matrand,2);-sum(matrand,1) sum(matrand(:))];
>> sum(mat1,1)
ans =
0 0 0 0 0 0 0 0 0 0
>> sum(mat1,2)
ans =
0
0
0
0
0
0

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