Exercise1

Determine whether the following matrices are diagonalizable. If so, find matrices \(D\) and \(P\) such that \(A=PDP^{-1}\text{.}\)

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

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

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

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