Q4 Diagonalize the given matrix \( A \) and hence find \( A^{2} \). \[ A=\left[\begin{array}{ccc} 10 & -2 & -5 \\ -2 & 2 & 3 \\ -5 & 3 & 5 \end{array}\right] \]
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The eigenvalues are the roots of the characteristic equation, which is given by det(A - λI) = 0, where I is the identity matrix and λ are the eigenvalues. For matrix A, we have: det(A - λI) = det([10-λ, -2, -5; -2, 2-λ, 3; -5, 3, 5-λ]) = 0 Solving this Show more…
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