Step 1: Finding characteristic equation.
Step 2: Finding eigenvalues. - The only eigenvalue is \( \lambda = 1 \) with algebraic multiplicity 3. - Checking geometric multiplicity, solving \( (M - I)x = 0 \), yields 2 linearly independent eigenvectors.
Step 3: Selecting the correct option. Since geometric multiplicity is 2, the correct answer is (C) 2.
If \[ A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix}, \] find \( A^{-1} \).
Using \( A^{-1} \), solve the following system of equations:
\[ \begin{aligned} 2x - 3y + 5z &= 11 \quad \text{(1)} \\ 3x + 2y - 4z &= -5 \quad \text{(2)} \\ x + y - 2z &= -3 \quad \text{(3)} \end{aligned} \]