###### Exercise 4

Suppose that \(A\) is a matrix with eigenvectors \(\vvec_1\) and \(\vvec_2\) and eigenvalues \(\lambda_1 = -1\) and \(\lambda_2=2\) as shown.

Sketch the vectors \(A\xvec\text{,}\) \(A^2\xvec\text{,}\) and \(A^{-1}\xvec\text{.}\)

Sketch the vectors \(A\xvec\text{,}\) \(A^2\xvec\text{,}\) and \(A^{-1}\xvec\text{.}\)