a 6x6 matrix with unkown x

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jad bousaid
jad bousaid on 22 Sep 2020
Commented: jad bousaid on 23 Sep 2020
i'm a civil engineering student and i'm having a problem solving a 6x6 matrix with an unkown x
the equation says ([K]-x[M])Φ=0
[M]= [(841*x)/10, 0, 0, 0, 0, 0]
[ 0, (841*x)/10, 0, 0, 0, 0]
[ 0, 0, (841*x)/10, 0, 0, 0]
[ 0, 0, 0, (841*x)/10, 0, 0]
[ 0, 0, 0, 0, (841*x)/10, 0]
[ 0, 0, 0, 0, 0, (841*x)/10]
[K]= 673000 -455000 77600 -654000 455000 12600
-455000 1810000 18000 445000 -321000 18000
77600 18000 429000 -12600 -18000 56875
-654000 455000 -12600 1070000 -455000 507000
455000 -321000 -18000 -455000 4480000 -18000
12600 18000 56875 507000 -18000 997750
first of all i need to calculate det(K-M) to find the 6 values of x, then replace it in M to calculate the vectors Φ
if someone can help me or tell me the method, it is very urgent and it is for my senior project.
thank you guys.

Answers (1)

Matt J
Matt J on 22 Sep 2020
See eig().
  1 Comment
jad bousaid
jad bousaid on 23 Sep 2020
root(z1^6 + z1^5*((2523*x)/5 - 13320750) + z1^4*(- 5601375375*x + (2121843*x^2)/20 + 64922447204375) + z1^3*(21839911239551750*x - 942151338075*x^2 + (594823321*x^3)/50 - 142154701436104375000) + z1^2*(- 35865631172329133812500*x + (5510209605738906525*x^2)/2 - (158469855064215*x^3)/2 + (1500739238883*x^4)/2000 + 140014161262115304725000000) + z1*(23550381924287794254745000000*x - 3016299581592880153631250*x^2 + (308939085228428025835*x^3)/2 - (26654629621800963*x^4)/8 + (1262121699900603*x^5)/50000 - 52141801798740670429625000000000) + (353814783205469041*x^6)/1000000 + 990293559916301748412027250000*x^2 - (22416543511934609883*x^5)/400 - 4385125531274090383131462500000000*x - 84556931603987073640129375*x^3 + (51963554135421593945447*x^4)/16 + 2945824239263437512080650000000000000, z1, 1)
root(z1^6 + z1^5*((2523*x)/5 - 13320750) + z1^4*(- 5601375375*x + (2121843*x^2)/20 + 64922447204375) + z1^3*(21839911239551750*x - 942151338075*x^2 + (594823321*x^3)/50 - 142154701436104375000) + z1^2*(- 35865631172329133812500*x + (5510209605738906525*x^2)/2 - (158469855064215*x^3)/2 + (1500739238883*x^4)/2000 + 140014161262115304725000000) + z1*(23550381924287794254745000000*x - 3016299581592880153631250*x^2 + (308939085228428025835*x^3)/2 - (26654629621800963*x^4)/8 + (1262121699900603*x^5)/50000 - 52141801798740670429625000000000) + (353814783205469041*x^6)/1000000 + 990293559916301748412027250000*x^2 - (22416543511934609883*x^5)/400 - 4385125531274090383131462500000000*x - 84556931603987073640129375*x^3 + (51963554135421593945447*x^4)/16 + 2945824239263437512080650000000000000, z1, 2)
root(z1^6 + z1^5*((2523*x)/5 - 13320750) + z1^4*(- 5601375375*x + (2121843*x^2)/20 + 64922447204375) + z1^3*(21839911239551750*x - 942151338075*x^2 + (594823321*x^3)/50 - 142154701436104375000) + z1^2*(- 35865631172329133812500*x + (5510209605738906525*x^2)/2 - (158469855064215*x^3)/2 + (1500739238883*x^4)/2000 + 140014161262115304725000000) + z1*(23550381924287794254745000000*x - 3016299581592880153631250*x^2 + (308939085228428025835*x^3)/2 - (26654629621800963*x^4)/8 + (1262121699900603*x^5)/50000 - 52141801798740670429625000000000) + (353814783205469041*x^6)/1000000 + 990293559916301748412027250000*x^2 - (22416543511934609883*x^5)/400 - 4385125531274090383131462500000000*x - 84556931603987073640129375*x^3 + (51963554135421593945447*x^4)/16 + 2945824239263437512080650000000000000, z1, 3)
root(z1^6 + z1^5*((2523*x)/5 - 13320750) + z1^4*(- 5601375375*x + (2121843*x^2)/20 + 64922447204375) + z1^3*(21839911239551750*x - 942151338075*x^2 + (594823321*x^3)/50 - 142154701436104375000) + z1^2*(- 35865631172329133812500*x + (5510209605738906525*x^2)/2 - (158469855064215*x^3)/2 + (1500739238883*x^4)/2000 + 140014161262115304725000000) + z1*(23550381924287794254745000000*x - 3016299581592880153631250*x^2 + (308939085228428025835*x^3)/2 - (26654629621800963*x^4)/8 + (1262121699900603*x^5)/50000 - 52141801798740670429625000000000) + (353814783205469041*x^6)/1000000 + 990293559916301748412027250000*x^2 - (22416543511934609883*x^5)/400 - 4385125531274090383131462500000000*x - 84556931603987073640129375*x^3 + (51963554135421593945447*x^4)/16 + 2945824239263437512080650000000000000, z1, 4)
root(z1^6 + z1^5*((2523*x)/5 - 13320750) + z1^4*(- 5601375375*x + (2121843*x^2)/20 + 64922447204375) + z1^3*(21839911239551750*x - 942151338075*x^2 + (594823321*x^3)/50 - 142154701436104375000) + z1^2*(- 35865631172329133812500*x + (5510209605738906525*x^2)/2 - (158469855064215*x^3)/2 + (1500739238883*x^4)/2000 + 140014161262115304725000000) + z1*(23550381924287794254745000000*x - 3016299581592880153631250*x^2 + (308939085228428025835*x^3)/2 - (26654629621800963*x^4)/8 + (1262121699900603*x^5)/50000 - 52141801798740670429625000000000) + (353814783205469041*x^6)/1000000 + 990293559916301748412027250000*x^2 - (22416543511934609883*x^5)/400 - 4385125531274090383131462500000000*x - 84556931603987073640129375*x^3 + (51963554135421593945447*x^4)/16 + 2945824239263437512080650000000000000, z1, 5)
root(z1^6 + z1^5*((2523*x)/5 - 13320750) + z1^4*(- 5601375375*x + (2121843*x^2)/20 + 64922447204375) + z1^3*(21839911239551750*x - 942151338075*x^2 + (594823321*x^3)/50 - 142154701436104375000) + z1^2*(- 35865631172329133812500*x + (5510209605738906525*x^2)/2 - (158469855064215*x^3)/2 + (1500739238883*x^4)/2000 + 140014161262115304725000000) + z1*(23550381924287794254745000000*x - 3016299581592880153631250*x^2 + (308939085228428025835*x^3)/2 - (26654629621800963*x^4)/8 + (1262121699900603*x^5)/50000 - 52141801798740670429625000000000) + (353814783205469041*x^6)/1000000 + 990293559916301748412027250000*x^2 - (22416543511934609883*x^5)/400 - 4385125531274090383131462500000000*x - 84556931603987073640129375*x^3 + (51963554135421593945447*x^4)/16 + 2945824239263437512080650000000000000, z1, 6)
i can't find the roots, all i can get is that.

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