# How do I found A-B*x which these matrix are 3x3

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Rommel Brito on 9 Sep 2020
Answered: Bruno Luong on 11 Sep 2020
A=[1231200 -615600 0; -615600 1231200 -615600; 0 -615600 615600]
A =
1231200 -615600 0
-615600 1231200 -615600
0 -615600 615600
B=[62.68 0 0; 0 62.68 0; 0 0 62.68]
B =
62.6800 0 0
0 62.6800 0
0 0 62.6800
And I want to get the A-Bx which x is a uknown variable that I want to know.

Walter Roberson on 9 Sep 2020
>> x=B\A
x =
19642.6292278239 -9821.31461391193 0
-9821.31461391193 19642.6292278239 -9821.31461391193
0 -9821.31461391193 9821.31461391193
>> A-B*x
ans =
0 0 0
0 0 0
0 0 0

Rommel Brito on 9 Sep 2020
In red is the Matrix A-Bx and in green is the result but i cant get the same result in matlab any idea?
Walter Roberson on 10 Sep 2020
A = [1231200, -615600, 0; -615600, 1231200, -615600; 0, -615600, 615600];
B = [62.68 0 0; 0 62.68 0; 0 0 62.68];
syms L
vals = solve(det(A - B*L), 'MaxDegree', 3);
real(vpa(vals)) %imaginary component is noise
Rommel Brito on 10 Sep 2020
Thank you! That worked!

Bruno Luong on 11 Sep 2020
Waoh, revise the theory of eigen vectors and linear algebra in general
Multiply a vector by a constant diagonal matrix is like multiply by the scalar.
This equation admits a solution for only when B = lambda*Identity where lambda is eigen value and x is the corresponding eigen eigen vector.
I'm surprises no one tell you that.