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Problem #5: Consider the following five statements about similar matrices. (1) If A and B are similar matrices, then det(4) = det(B). (11) If A and B are similar matrices and A is symmetric, then B is symmetric. (111) If A and B are similar matrices, then A and B have the same eigenvalues. (iv) If A and B are similar matrices, then at least one of A and B is a triangular matrix. (v) If A and B are similar matrices, then A² and B² are similar. 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).

Problem #5: Consider the following five statements about similar matrices. (1) If A and B are similar matrices, then det(4) = det(B). (11) If A and B are similar matrices and A is symmetric, then B is symmetric. (111) If A and B are similar matrices, then A and B have the same eigenvalues. (iv) If A and B are similar matrices, then at least one of A and B is a triangular matrix. (v) If A and B are similar matrices, then A² and B² are similar. 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).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 19EQ
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Problem #5: Consider the following five statements about similar matrices. (1) If A and B are similar matrices, then det(4) = det(B). (ii) If A and B are similar matrices and A is symmetric, then B is symmetric. (111) If A and B are similar matrices, then A and B have the same eigenvalues. (iv) If A and B are similar matrices, then at least one of A and B is a triangular matrix. (v) If A and B are similar matrices, then A² and B² are similar. 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. (1) If A and B are similar matrices, then det(4) = det(B). (ii) If A and B are similar matrices and A is symmetric, then B is symmetric. (111) If A and B are similar matrices, then A and B have the same eigenvalues. (iv) If A and B are similar matrices, then at least one of A and B is a triangular matrix. (v) If A and B are similar matrices, then A² and B² are similar. 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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