1. Diagonalize $\begin{pmatrix} -12 & 15 \ -10 & 13 \end{pmatrix}$.
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The characteristic polynomial is $$\begin{vmatrix} -12-\lambda & 15 \\ -10 & 13-\lambda \end{vmatrix} = (-12-\lambda)(13-\lambda) - (-10)(15) = \lambda^2 - \lambda - 3.$$ The roots of this polynomial are $$\lambda = \frac{1 \pm \sqrt{1 + 12}}{2} = \frac{1 \pm Show more…
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