Show that the matrix is not diagonalizable. 3 -1 4 3 0 4 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (A1, 12) = 3,4 STEP 2: Find the eigenvectors x1 and x2 corresponding to À, and A2, respectively. X1 = -1 X, = STEP 3: Since the matrix does not have three v 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
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Show that the matrix is not diagonalizable.
3 -1
4
3
0 4
STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.)
(A1, 12) =
3,4
STEP 2: Find the eigenvectors x1 and x2 corresponding to À, and A2, respectively.
X1 =
-1
X, =
STEP 3: Since the matrix does not have three
v linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
Transcribed Image Text:Show that the matrix is not diagonalizable. 3 -1 4 3 0 4 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (A1, 12) = 3,4 STEP 2: Find the eigenvectors x1 and x2 corresponding to À, and A2, respectively. X1 = -1 X, = STEP 3: Since the matrix does not have three v linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
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