4x -5y-11z=12,.
x-3y+z=1
2x + 3y-7z = 2

Answer

To solve the system of linear equations given by:

1. \( 4x - 5y - 11z = 12 \)
2. \( x - 3y + z = 1 \)
3. \( 2x + 3y - 7z = 2 \)

we can use the matrix method. Here are the steps to find the values of \( x \), \( y \), and \( z \):

### Step 1: Write the equations in matrix form

We can express the system of equations in the form \( AX = B \), where:

\[ A = \begin{pmatrix} 4 & -5 & -11 \\ 1 & -3 & 1 \\ 2 & 3 & -7 \end{pmatrix}, \quad X = \begin{pmatrix} x \\ y \\ z \end{pmatrix}, \quad B = \begin{pmatrix} 12 \\ 1 \\ 2 \end{pmatrix} \]