How to get solution to make this determinant zero?

Question

A = [A-x(1) B-x(2) C-x(3);D-x(4) E-x(5) F-x(6); G-x(7) H-x(8) I-x(9)]

I have to obtain x(1)...x(9) for det(A) = 0.

you have A(matrix) = [A - x(1) ....] This A inside is also the same matrix? — GameOfThrows, Nov 05 '15 at 09:15

score 4 · Accepted Answer · answered Nov 05 '15 at 09:35

Given a 3x3 matrix A

its determinant is

therefore you need to solve |A| = 0. For your case we are given

The easiest solution for x so that |A| = 0 is when

a - x(1) = 0
b - x(2) = 0
c - x(3) = 0

which leads to

x(1) = a
x(2) = b
x(3) = c

so

x = A

is the most trivial solution. There exists an infinite number of solutions to this problem, this is just one. You could choose another solution where

a - x(1) != 0
b - x(2) != 0
c - x(3) != 0

and then you would have to set

ei - fh = 0
di - fg = 0
dh - eg = 0

which would involve simultaneous equations.

I suggest before trying to code up a solution you work through one by hand like I've done here.

thank you for your answer. But, a - x(1) != 0 b - x(2) != 0 c - x(3) != 0 and ei - fh != 0 di - fg != 0 dh - eg != 0 So I think, I have to use optimizat algorithm to minimize det(A)... — Moussekim, Nov 05 '15 at 10:37
Your comment is unclear are you saying you can't choose `x = A`, if so that would have been some very important information to include in the original question. — IKavanagh, Nov 05 '15 at 10:41

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