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Cramer's Rule is a numerical method for solving a system of linear equations using determinants. Given the system: \[ \begin{aligned} x + 2y + z &= 3 \\ 2x - y + 2z &= 1 \\ 3x + y + z &= 0 \end{aligned} \] ### Step 1: Represent the system in matrix form The system can be written as: \[ A \cdot X = B \] where: \[ A = \begin{bmatrix} 1 & 2 & 1 \\ 2 & -1 & 2 \\ 3 & 1 & 1 \end{bmatrix} \] \[ X = \begin{bmatrix} x \\ y \\ z \end{bmatrix} \] \[ B = \begin{bmatrix} 3 \\ 1 \\ 0 \end{bmatrix} \] ### Step 2: Compute Determinant of ___ ___ ______ ________ ______ _________.
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