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Cramer's Rule is applicable to a system of linear equations Ax = b if and only if the determinant of the coefficient matrix A is nonzero (det(A) ≠ 0). Let's check if it applies to the given system. ### Step 1: Write the system in matrix form The given system is: \[ \begin{aligned} x + y + z &= \pi \\ - \pi x + \pi + \sqrt{2}z &= 0 \\ \pi^2 x + \pi^2 y + 2z &= 0 \end{aligned} \] Rewriting the second equation: \[ - \pi x + \sqrt{2}z = -\pi \] Now, the coefficient matrix A and constant matrix b are: \[ A = \begin{bmatrix} 1 & 1 & 1 \\ -\pi & 0 & \sqrt{2} \\ \pi^2 & \pi^2 & 2 \end{bmatrix} \] \[ b = \begin{bmatrix} \pi _____ _______ ______ ______ _______ ________ ____ __________ ________.
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