Questions: -2x-y-z+5=0 -x-2y-z+10=0 -x-y-2z+8=0

To solve this system of linear equations, we can use matrix operations. Specifically, we can represent the system as a matrix equation \(AX = B\) and then solve for \(X\) using the inverse of matrix \(A\) or other numerical methods.

Dado el sistema de ecuaciones: \[ \begin{array}{l} -2x - y - z + 5 = 0 \\ -x - 2y - z + 10 = 0 \\ -x - y - 2z + 8 = 0 \end{array} \] Podemos reescribirlo en forma matricial \(AX = B\), donde: \[ A = \begin{bmatrix} -2 & -1 & -1 \\ -1 & -2 & -1 \\ -1 & -1 & -2 \end{bmatrix}, \quad B = \begin{bmatrix} -5 \\ -10 \\ -8 \end{bmatrix} \]

Al resolver el sistema, encontramos que: \[ X = \begin{bmatrix} -0.75 \\ 4.25 \\ 2.25 \end{bmatrix} \] Esto implica que: \[ x = -0.75, \quad y = 4.25, \quad z = 2.25 \]

Los valores de las variables son: \[ x = -\frac{3}{4}, \quad y = \frac{17}{4}, \quad z = \frac{9}{4} \]

\[ \boxed{x = -\frac{3}{4}, \, y = \frac{17}{4}, \, z = \frac{9}{4}} \]