Given the system of equation: \[ \begin{array}{r}2 x_{1}-x_{2}+x_{3}=11 \\ -x_{1}-x_{3}=2 \\ -x_{1}+2 x_{2}+x_{3}=-4\end{array} \] a) Write the system of equations in matrix form \( \mathrm{AX}=\mathrm{B} \).

To express the given system of equations in matrix form \( \mathrm{AX} = \mathrm{B} \), we identify the coefficients of the variables and the constants on the right side of the equations. The equations are: 1. \( 2x_1 - x_2 + x_3 = 11 \) 2. \( -x_1 + 0x_2 - x_3 = 2 \) 3. \( -x_1 + 2x_2 + x_3 = -4 \) From these equations, we can form the following matrices: - Coefficient matrix \( \mathrm{A} \): \[ \mathrm{A} = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 0 & -1 \\ -1 & 2 & 1 \end{bmatrix} \] - Variable matrix \( \mathrm{X} \): \[ \mathrm{X} = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \] - Constant matrix \( \mathrm{B} \): \[ \mathrm{B} = \begin{bmatrix} 11 \\ 2 \\ -4 \end{bmatrix} \] Putting it all together, we have the matrix form: \[ \mathrm{AX} = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 0 & -1 \\ -1 & 2 & 1 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 11 \\ 2 \\ -4 \end{bmatrix} \]