Answer
$x= -1; y= 2; z= 0$
Work Step by Step
A system of equations can be written in the form: $AX=B$
where $B= \begin{bmatrix} x \\ y \\ z \end{bmatrix}$
When there exists an inverse of a matrix, the following relationship is true:
$A A^{-1} = I$
Thus, $X=A^{-1} B = \begin{bmatrix} 2& 3 & 5 \\ 3 & 5 & 9 \\ 5 & 9 & 17 \end{bmatrix} \begin{bmatrix} 4 \\ 7 \\ 13 \end{bmatrix} $
Now, we will use the Row Reduced Echelon Form.
$X= \begin{bmatrix} 1 & 0 & -2 & : & -1 \\ 0 & 1 & 3 & : & 2 \\0 & 0 & 0 & : & 0 \end{bmatrix}$
Therefore, $x= -1; y= 2; z= 0$
