Ononot — Let A be a 2 \times 2 symmetric matrix with eigenvalues \lam

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Eigenvalues & Eigenvectorshard

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Let $A$ be a $2 \times 2$ symmetric matrix with eigenvalues $\lambda_1 = 3, \lambda_2 = 5$ . Consider the $4 \times 4$ block matrix $M = \begin{pmatrix} I_2 & A \\ A & I_2 \end{pmatrix}$ . What are the eigenvalues of $M$ ?