25. Proof Prove that if A and B are similar matrices, then |A| = |B|. Is the converse true? Answer 26. Illustrate the result of Exercise 25 using the matrices 1 0 01 A = 0 P = 0-2 0 0,B: where B=P-¹ AP. 03 -1 1 0] 2 1 2, P-1 = 11 11 7 10] 10 8 10 -18 -12 -17. -1 -1 21 0-1 2 1 2-3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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25. Proof Prove that if A and B are similar matrices, then |A| = |B|.
Is the converse true?
Answer
26. Illustrate the result of Exercise 25 using the matrices
A =
P =
1 0 01
B=
0-2 0,B:
0 03
-1 1 0]
where B=P-¹ AP.
2 1 2, P-1
1 1
11 7 10]
10
8 10
-18 -12 -17]
-1 -1 21
0-1
1
2
2-3
Transcribed Image Text:25. Proof Prove that if A and B are similar matrices, then |A| = |B|. Is the converse true? Answer 26. Illustrate the result of Exercise 25 using the matrices A = P = 1 0 01 B= 0-2 0,B: 0 03 -1 1 0] where B=P-¹ AP. 2 1 2, P-1 1 1 11 7 10] 10 8 10 -18 -12 -17] -1 -1 21 0-1 1 2 2-3
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