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matlaboptimizationdeterminants

How to get solution to make this determinant zero?

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.

Solution

  • Given a 3x3 matrix A

                                                     <code>A</code> matrix

    its determinant is

                                       |A|

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

                                       A - x

    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.