Show that the matrix is not diagonalizable. 2 −4 2 0 2 3 0 0 3 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (?1, ?2) = STEP 2: Find the eigenvectors x1 and x2 corresponding to ?1 and ?2, respectively. x1 = x2 = STEP 3: Since the matrix does not have linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable. linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
Show that the matrix is not diagonalizable. 2 −4 2 0 2 3 0 0 3 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (?1, ?2) = STEP 2: Find the eigenvectors x1 and x2 corresponding to ?1 and ?2, respectively. x1 = x2 = STEP 3: Since the matrix does not have linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable. linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Show that the matrix is not diagonalizable.
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2 | −4 | 2 |
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| 0 | 2 | 3 | ||||
| 0 | 0 | 3 |
| STEP 1: | Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) | |
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(?1, ?2) =
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| STEP 2: | Find the eigenvectors x1 and x2 corresponding to ?1 and ?2, respectively. | |||
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| x2 | = |
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| STEP 3: | Since the matrix does not have linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable. |
linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
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