Find a 3 3 symmetric matrix that has eigenvalues l1 1, l2 3, and l3 5 and corresponding

Chapter 8, Problem 36

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Find a \(3 \times 3\) symmetric matrix that has eigenvalues \(\lambda_{1}=1\), \(\lambda_{2}=3, \text { and } \lambda_{3}=5\) and corresponding eigenvectors

\(\mathbf{K}_{1}=\left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right), \mathbf{K}_{2}=\left(\begin{array}{r} 1 \\ 0 \\ -1 \end{array}\right), \text { and } \mathbf{K}_{3}=\left(\begin{array}{l} 1 \\ 2 \\ 1 \end{array}\right) \)

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