Diagonalization (Linear Algebra)
Free printable university Linear Algebra worksheet on diagonalizing 2x2 and 3x3 matrices as A = PDP^-1, including a defective matrix that cannot be diagonalized.
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Linear Algebra · Math worksheet
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Linear Algebra: Diagonalization
Decide whether each matrix is diagonalizable. If it is, give an invertible P (its columns are eigenvectors) and diagonal D (the matching eigenvalues) with A = PDP⁻¹; if not, explain why using the eigenvalue multiplicities. Matrices are written in row form, e.g. [1, 2; 3, 4].
- 1.Diagonalize A = [2, 0; -2, 3] if possible: find an invertible P and a diagonal D with A = PDP⁻¹, or explain why none exist.
- 2.Diagonalize A = [2, 1; 0, 2] if possible: find an invertible P and a diagonal D with A = PDP⁻¹, or explain why none exist.
- 3.Diagonalize A = [1, -1, 1; -16, -8, -8; 22, 14, 10] if possible: find an invertible P and a diagonal D with A = PDP⁻¹, or explain why none exist.
- 4.Diagonalize A = [-2, -1; 0, -1] if possible: find an invertible P and a diagonal D with A = PDP⁻¹, or explain why none exist.
- 5.Diagonalize A = [-1, 1; -1, -3] if possible: find an invertible P and a diagonal D with A = PDP⁻¹, or explain why none exist.
- 6.Diagonalize A = [-1, 2, 4; -18, 0, 6; 4, 4, 5] if possible: find an invertible P and a diagonal D with A = PDP⁻¹, or explain why none exist.
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