Question

2x+y-z=8

-3x-y+2z=-11

-2x+y+2z=-3

Answer 1

$2x+y-z=8\\ -3x-y+2z=-11\\ -2x+y+2z=-3\\ \begin{pmatrix} 2 & 1&-1&|&8 \\ -3 & -1&2&|&-11\\ -2&1&2&|&-3 \end{pmatrix}\to$

IIr+Ir($\frac{3}{2}$ )

IIIr+Ir

$\to\begin{pmatrix} 2 & 1&-1&|&8 \\ 0& \frac{1}{2}&\frac{1}{2}&|&1\\ 0&2&1&|&5 \end{pmatrix}\to$

IIr(2)

IIIr+IIr(-2)

$\to\begin{pmatrix} 2 & 1&-1&|&8 \\ 0 & 1&1&|&2\\ 0&0&-1&|&1 \end{pmatrix}\to$

IIIr(-1)

IIr+IIIr(-1)

Ir+IIIr(1)

$\to\begin{pmatrix} 2 & 1&0&|&7 \\ 0 & 1&0&|&3\\ 0&0&1&|&-1 \end{pmatrix}\to$

Ir+IIr(-1)

$\to\begin{pmatrix} 2 & 0&0&|&4 \\ 0 & 1&0&|&3\\ 0&0&1&|&-1 \end{pmatrix}\to$

Ir($\frac{1}{2}$ )

$\to\begin{pmatrix} 1& 0&0&|&2 \\ 0 & 1&0&|&3\\ 0&0&1&|&-1 \end{pmatrix}$

$x=2,y=3,z=-1\\(2,3,-1)$