Ononot — A 2 \times 2 matrix A has eigenvalues \lambda1 = 5 and \lamb

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Eigenvalues & Eigenvectorseasy

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A $2 \times 2$ matrix $A$ has eigenvalues $\lambda_1 = 5$ and $\lambda_2 = 3$ , with eigenvectors $v_1 = \begin{pmatrix} 2 \\ 1 \end{pmatrix}$ and $v_2 = \begin{pmatrix} 1 \\ 1 \end{pmatrix}$ respectively. If $A = PDP^{-1}$ , what is the diagonal matrix $D$ ?