Solved: In 16, determine which of the indicated column vectors are eigenvectors of the
Chapter 8, Problem 5(choose chapter or problem)
In Problems 1–6, determine which of the indicated column vectors are eigenvectors of the given matrix A. Give the corresponding eigenvalue.
\(\begin{array}{l} \mathbf{A}=\left(\begin{array}{rrr} 1 & -2 & 2 \\ -2 & 1 & -2 \\ 2 & 2 & 1 \end{array}\right) ; \quad \mathbf{K}_{1}=\left(\begin{array}{l} 0 \\ 1 \\ 1 \end{array}\right), \\ \mathbf{K}_{2}=\left(\begin{array}{r} 4 \\ -4 \\ 0 \end{array}\right), \quad \mathbf{K}_{3}=\left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right) \end{array}\)
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