Show that the matrix is not diagonalizable. 1-1 4 1 2 0 2 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (d1, 22) = | STEP 2: Find the eigenvectors x, and x2 corresponding to A and A2, respectively. X = X = STEP 3: Since the matrix does not have -Select---V Ilinearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.5: Iterative Methods For Computing Eigenvalues
Problem 3EQ
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Show that the matrix is not diagonalizable.
1 -1 4
1 2
0 2
STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.)
(d1, 22) =
STEP 2: Find the eigenvectors x, and x2 corresponding to Ay and A2, respectively.
X1 =
X2 =
STEP 3: Since the matrix does not have -Select--V linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
Transcribed Image Text:Show that the matrix is not diagonalizable. 1 -1 4 1 2 0 2 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (d1, 22) = STEP 2: Find the eigenvectors x, and x2 corresponding to Ay and A2, respectively. X1 = X2 = STEP 3: Since the matrix does not have -Select--V linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
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