Consider the following. 1 1 0 5 0 1 A 0 4 -2 4-2 1 2 (a) Verify that A is diagonalizable by computing PAP. p-AP = (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n xn matrices, then they have the same eigenvalues.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Consider the following.
1 1
0 5
0 1
A
0 4
-2 4-2
1 2
(a) Verify that A is diagonalizable by computing PAP.
p-AP =
(b) Use the result of part (a) and the theorem below to find the eigenvalues of A.
Similar Matrices Have the Same Eigenvalues
If A and B are similar n xn matrices, then they have the same eigenvalues.
Transcribed Image Text:Consider the following. 1 1 0 5 0 1 A 0 4 -2 4-2 1 2 (a) Verify that A is diagonalizable by computing PAP. p-AP = (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n xn matrices, then they have the same eigenvalues.
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