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What's on the worksheet
- Decide whether each matrix is diagonalizable with real P and D, and give the reason.
- Diagonalize the matrix below:
- A sequence follows the rule a_n = 5a_n-1 - 6a_n-2 for n ≥ 2, with a_0 = -1 and a_1 = -5.
- The matrix A = \begin{bmatrix} 5 & 4 & -4 \\ 5 & 3 & -5 \\ 7 & 4 & -6 \end{bmatrix} has eigenvalues 1, 3 and −2.
- The matrix A = \begin{bmatrix} 2 & -2 & 1 \\ 1 & -1 & 1 \\ 2 & -4 & 3 \end{bmatrix} has characteristic polynomial -( - 1)²( - 2).
- True or false?
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Diagonalization: the lesson ›