Find a and b in a matrix

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I was wondering if I could have some help / pointers in the right direction..

I've been given a simultaneous equations as follows:

  1. $x_1 + x_2 = 0$
  2. $-ax_1 - 2ax_1 + (a^2-1)x_3 = 1$
  3. $ax_1 + ax_2 + 2ax_3 = b+3$

I've put it in a matrix and used Gaussian elimination to find the values of $x_1,x_2$ and $x_3$ as $(b+4)/a$, $-(b+4)/a$ and $b/2 +3/2$.

Assume $a ≠ 0$ find the general solution for the system of equations, have I done that already when I the 'found' the values for $x_1,x_2$ and $x_3$?

In-addition when $a = 0$ what is the values of $b$? For $ax_1 + ax_2 +2ax_3 = b+3$ if $a$ is zero I find $b$ to be $-3$.

Am I on the right lines?