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Questions and Answers
If A = P^{-1}BP, then what can be concluded about the eigenvalues of A and B?
If A = P^{-1}BP, then what can be concluded about the eigenvalues of A and B?
- A has more eigenvalues than B
- A and B have the same eigenvalues (correct)
- A and B have different eigenvalues
- B has more eigenvalues than A
If λ is an eigenvalue of A, what can be said about λ as an eigenvalue of B?
If λ is an eigenvalue of A, what can be said about λ as an eigenvalue of B?
- λ is not an eigenvalue of B
- There is not enough information to determine the relationship between λ as eigenvalues of A and B
- λ is also an eigenvalue of B (correct)
- λ may or may not be an eigenvalue of B
What role does P~x play in the given proof?
What role does P~x play in the given proof?
- Scalar multiple
- Identity matrix
- Zero vector
- Eigenvector (correct)
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