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Matrices

Eigenvalues and Eigenvectors

         

Find the eigenvalues of the matrix \[ A = \begin{pmatrix} 8 & 0 & 0 \\6 & 6 & 11 \\ 1 & 0 & 1 \end{pmatrix}. \]

What is the sum of eigenvalues of the transformation matrix \[ A = \begin{pmatrix} 8 & 2 \\ 2 & 8 \end{pmatrix}? \]

Given the transformation matrix \( A = \begin{pmatrix} 5 & 4 \\ 4 & 5 \end{pmatrix}, \) which of the following are the eigenvectors of \( A?\)

Which of the following are the eigenvectors of the transformation matrix \[ A = \begin{pmatrix} 8 & 4 \\ 1 & 5 \end{pmatrix}?\]

Which of the following can't be an eigenvector of the transformation matrix \[ A = \begin{pmatrix} 8 & 0 & 0 \\ 3 & 5 & 0 \\ 3 & 2 & 3 \end{pmatrix}? \]

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