Answer
$x_1= -1; x_2=3; x_3= 2$
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, $X=A^{-1} B = \begin{bmatrix} 4&-1& 1 \\ 2 & 2 & 3 \\ 5 &-2& 6 \end{bmatrix} \begin{bmatrix} -5 \\ 10 \\ 1 \end{bmatrix} = \begin{bmatrix} -1 \\ 3 \\ 2 \end{bmatrix}$
So, $X= \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}= \begin{bmatrix} -1 \\ 3 \\ 2 \end{bmatrix}$
Therefore, $x_1= -1; x_2=3; x_3= 2$
