Exercise 2

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

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

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

3. $A= \left[\begin{array}{rrrr} 1.9 & -16.0 & -13.0 & 27.0 \\ -2.4 & 20.3 & 4.6 & -17.7 \\ -0.51 & -11.7 & -1.4 & 13.1 \\ -2.1 & 15.3 & 6.9 & -20.5 \\ \end{array}\right]$.