+26396 x + y − z = −5
x + 2y + 3z = −12
2x − y − 13z = 13
\(\text{Let Matrix } A = \begin{pmatrix} 1 & 1 & -1 \\ 1 & 2 & 3 \\ 2 & -1 & -13 \end{pmatrix}\)
\(\text{Let } \vec{r} = \begin{pmatrix} -5 \\ -12 \\ 13 \end{pmatrix}\)
\(\text{Let } \vec{x} = \begin{pmatrix} x \\ y \\ z \end{pmatrix}\)
\(\text{Let Matrix } A^{-1} = \begin{pmatrix} -23 & 14 & 5 \\ 19 & -11 & -4 \\ -5 & 3 & 1 \end{pmatrix}\)
Then
\(\begin{array}{|rcll|} \hline A\vec{x} &=& \vec{r} \\ \vec{x} &=& A^{-1}\vec{r} \\ \vec{x} &=& \begin{pmatrix} -23 & 14 & 5 \\ 19 & -11 & -4 \\ -5 & 3 & 1 \end{pmatrix}\cdot \begin{pmatrix} -5 \\ -12 \\ 13 \end{pmatrix} \\ \vec{x} &=& \begin{pmatrix} 12 \\ -15 \\ 2 \end{pmatrix} \\ \hline \end{array} \)
x = 12
y = -15
z = 2
