<s>[INST] Solving a system of three linear equations with three unknowns Is my working correct or am I completely wrong? Have I missed anything out? Any feedback is appreciated.
Question: Consider the following system of equations
$2x + 2y + z = 2$
$−x + 2y − z = −5$
$x − 3y + 2z = 8$
Form an augmented matrix, then reduce this matrix to reduced row echelon form and solve the system.
My answer/working: 
Given:
$2x + 2y + z = 2$
$-x + 2y - z = -5$
$x - 3y + 2z = 8$
Matrix form: 
$\begin{pmatrix} 2 & 2 & 1 & 2\\ -1 & 2 & -1 & -5 \\ 1& -3& 2 & 8 \end{pmatrix}$

$\begin{pmatrix}2 & 0 & 0 & 2\\ 0 & 3 & 0 & -3\\ 0 & 0 & \frac56 & \frac53\end{pmatrix}$
Solution: $x = 1; y = -1; z = 2;$
 [/INST] You can reduce your matrix further. remember that you can multiply and/or divide each row so you end up obtaining
$$
\begin{pmatrix}
     1  &   0  &   0  &   1\\
     0  &  1   &  0  &  -1\\
     0  &   0  &   1   &  2\\ 
\end{pmatrix}
$$ 
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