If A and B are n x n matrices, we say that B is similar to A if there is an invertible matrix P such that B=P-¹AP. We'll be working more with this definition in class. As a starting point, we ask you to prove a couple facts. Prove: If A and B are similar, then they have the same determinant. Use complete a. b. sentences. Prove: The only matrix similar to In is In. In other words, if C is a matrix that is similar to In, then C must be equal to In. Use complete sentences.
If A and B are n x n matrices, we say that B is similar to A if there is an invertible matrix P such that B=P-¹AP. We'll be working more with this definition in class. As a starting point, we ask you to prove a couple facts. Prove: If A and B are similar, then they have the same determinant. Use complete a. b. sentences. Prove: The only matrix similar to In is In. In other words, if C is a matrix that is similar to In, then C must be equal to In. Use complete sentences.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve both parts correctly
Transcribed Image Text:If A and B are nxn matrices, we say that B is similar to A if there is an invertible
matrix P such that B=P-¹AP. We'll be working more with this definition in class. As a starting
point, we ask you to prove a couple facts.
Prove: If A and B are similar, then they have the same determinant. Use complete
a.
b.
sentences.
Prove: The only matrix similar to In is In. In other words, if C is a matrix that is
similar to In, then C must be equal to In. Use complete sentences.
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