Exercise2

Determine whether the following matrices have complex eigenvalues. If so, find the matrix \(C\) such that \(A = PCP^{-1}\text{.}\)

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

  2. \(A = \left[\begin{array}{rr} -1 \amp 1 \\ -1 \amp -3 \\ \end{array}\right] \text{.}\)

  3. \(A = \left[\begin{array}{rr} 3 \amp -4 \\ 2 \amp -1 \\ \end{array}\right] \text{.}\)

in-context