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Matrices

Eigenvalues and Eigenvectors

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

1 \text{ or } 6 \text{ or } 8

6 \text{ or } 8 \text{ or } 11

0 \text{ or } 1 \text{ or } 8

7 \text{ or } 14 \text{ or } 19

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by Brilliant Staff

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

19

16

10

4

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by Brilliant Staff

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

\begin{pmatrix} 5 \\ 5 \end{pmatrix} \text{ and } \begin{pmatrix} 4 \\ -4 \end{pmatrix}

\begin{pmatrix} 1 \\ 1 \end{pmatrix} \text{ and } \begin{pmatrix} -1 \\ 1 \end{pmatrix}

\begin{pmatrix} 5 \\ 4 \end{pmatrix} \text{ and } \begin{pmatrix} 5 \\ -4 \end{pmatrix}

\begin{pmatrix} 1 \\ 0 \end{pmatrix} \text{ and } \begin{pmatrix} 0 \\ -1 \end{pmatrix}

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by Brilliant Staff

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

\begin{pmatrix} 4 \\ 1 \end{pmatrix} \text{ and } \begin{pmatrix}1 \\ 4 \end{pmatrix}

\begin{pmatrix} 4 \\ 1 \end{pmatrix} \text{ and } \begin{pmatrix}1 \\ -1 \end{pmatrix}

\begin{pmatrix} -1 \\ 1 \end{pmatrix} \text{ and } \begin{pmatrix}1 \\ 1 \end{pmatrix}

\begin{pmatrix} 4 \\ 1 \end{pmatrix} \text{ and } \begin{pmatrix}-4 \\ 1 \end{pmatrix}

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by Brilliant Staff

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

\begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix}

\begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}

\begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}

\begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}

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by Brilliant Staff