Problem #5: the following five state ents about similar (i) If A and B are similar matrices, then 4² and B² are similar. (ii) If A and B are similar matrices, then at least one of A and B is a triangular matrix. (iii) If A and B are similar matrices and A is symmetric, then B is symmetric. (iv) If A and B are similar matrices, then det(A) = det(B). (v) If A and B are similar matrices, then A and B have the same eigenvalues. Determine which which statements are true (1) or false (2) by testing out each statement on an appropriate m So, for example, if you think that the answers, in the above order, are True,False,False, True,False, then you enter '1,2,2,1,2' into the answer box below (without the quotes).

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 7CC: If A and B are matrices with the same dimension and k is a real number, how do you find A+B and kA ?
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Problem #5: Consider the following five statements about similar matrices.
(i) If A and B are similar matrices, then A2 and B2 are similar.
(ii) If A and B are similar matrices, then at least one of A and B is a triangular matrix.
Problem #5:
(iii) If A and B are similar matrices and A is symmetric, then B is symmetric.
(iv) If A and B are similar matrices, then det(A) = det(B).
(v) If A and B are similar matrices, then A and B have the same eigenvalues.
Determine which which statements are true (1) or false (2) by testing out each statement on an appropriate matrix.
So, for example, if you think that the answers, in the above order, are True,False,False, True,False, then you would
enter '1,2,2,1,2' into the answer box below (without the quotes).
Transcribed Image Text:Problem #5: Consider the following five statements about similar matrices. (i) If A and B are similar matrices, then A2 and B2 are similar. (ii) If A and B are similar matrices, then at least one of A and B is a triangular matrix. Problem #5: (iii) If A and B are similar matrices and A is symmetric, then B is symmetric. (iv) If A and B are similar matrices, then det(A) = det(B). (v) If A and B are similar matrices, then A and B have the same eigenvalues. Determine which which statements are true (1) or false (2) by testing out each statement on an appropriate matrix. So, for example, if you think that the answers, in the above order, are True,False,False, True,False, then you would enter '1,2,2,1,2' into the answer box below (without the quotes).
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