Exercise1

For each of the following matrices, find its characteristic polynomial, its eigenvalues, and the multiplicity of each eigenvalue.

  1. \(A=\left[\begin{array}{rr} 4 \amp -1 \\ 4 \amp 0 \\ \end{array}\right] \text{.}\)

  2. \(A=\left[\begin{array}{rrr} 3 \amp -1 \amp 3 \\ 0 \amp 4 \amp 0 \\ 0 \amp 0 \amp -6 \end{array}\right] \text{.}\)

  3. \(A = \left[\begin{array}{rr} -2 \amp 0 \\ 0 \amp -2 \\ \end{array}\right] \text{.}\)

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

in-context