For the matrix A, find (if possible) a nonsingular matrix P such that P-¹AP is diagonal. (If not possible, enter IMPOSSIBLE.) 2-2 5 0 3 -2 0 -1 2 A = -3 0 -2 41888 P = P-¹AP = 2 0 Verify that P-¹AP is a diagonal matrix with the eigenvalues on the main diagonal. 0 X Need Help? -1/2 1/3 -1/3 9/2 Read It -1/2 -2/3 → 11/3 → -

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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For the matrix A, find (if possible) a nonsingular matrix P such that P-¹AP is diagonal. (If not possible, enter IMPOSSIBLE.)
2-2 5
0 3 -2
0 -1 2
P =
A =
1
0
10
p-¹AP =
2
0
0
-3
1
X
Need Help?
1
11
Verify that P-¹AP is a diagonal matrix with the eigenvalues on the main diagonal.
-1/2
1/3
-1/3
Read It
9/2
11
-2
-1/2
-2/3
→
11/3
→
Transcribed Image Text:For the matrix A, find (if possible) a nonsingular matrix P such that P-¹AP is diagonal. (If not possible, enter IMPOSSIBLE.) 2-2 5 0 3 -2 0 -1 2 P = A = 1 0 10 p-¹AP = 2 0 0 -3 1 X Need Help? 1 11 Verify that P-¹AP is a diagonal matrix with the eigenvalues on the main diagonal. -1/2 1/3 -1/3 Read It 9/2 11 -2 -1/2 -2/3 → 11/3 →
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