Exercise2

Use the commands power, inverse_power, and find_closest_eigenvalue to approximate the eigenvalues and associated eigenvectors of the following matrices.

1. $$A= \left[\begin{array}{rr} -2 \amp -2 \\ -8 \amp -2 \\ \end{array}\right] \text{.}$$

2. $$A= \left[\begin{array}{rr} 0.6 \amp 0.7 \\ 0.5 \amp 0.2 \\ \end{array}\right] \text{.}$$

3. $$A= \left[\begin{array}{rrrr} 1.9 \amp -16.0 \amp -13.0 \amp 27.0 \\ -2.4 \amp 20.3 \amp 4.6 \amp -17.7 \\ -0.51 \amp -11.7 \amp -1.4 \amp 13.1 \\ -2.1 \amp 15.3 \amp 6.9 \amp -17.5 \\ \end{array}\right] \text{.}$$

in-context