# Quiz Chapter 10: Eigenvalues and Eigenvectors

 MULTIPLE CHOICE TEST EIGENVALUES AND EIGENVECTORS

1. The eigenvalues of $\begin{bmatrix} 5&6&17 \\ 0&-19&23 \\ 0&0&37 \\ \end{bmatrix}$ are

2. If $\begin{bmatrix} -4.5\\-4\\1\\ \end{bmatrix}$ is an eigenvector of $\begin{bmatrix} 8&-4&2 \\ 4&0&2 \\ 0&-2&-4 \\ \end{bmatrix}$, the eigenvalue corresponding to the eigenvector is

3. The eigenvalues of the following matrix $\begin{bmatrix} 3&2&9 \\ 7&5&13 \\ 6&17&19 \\ \end{bmatrix}$ are given by solving the cubic equation

4. The eigenvalues of a $4 \times 4$ matrix $\left[ A \right]$ are given as $2, \, -3, \, 13,$ and $7$. The |det$(A)$| then is

5. If one of the eigenvalues of $\left[ A \right]_{n \times n}$ is zero, it implies

6. Given that matrix $\left[ A \right] = \begin{bmatrix} 8&-4&2 \\ 4&0&2 \\ 0&-2&-3 \\ \end{bmatrix}$ has an eigenvalue  value of $4$ with the corresponding eigenvectors of $\left[ x \right] = \begin{bmatrix} -4.5 \\ -4 \\ 1 \\ \end{bmatrix}$, then $\left[ A \right]^{5} \left[ X \right]$ is