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4. Give an example of a 3 x 3 matrix A such that neither A nor A² is the zero matrix, but A³ = 0. 5. Find all examples of matrices A which commute with both B = (6%) 0 and C = 00 0 (8 5) That is, find all matrices A so that AB = BA and AC = CA. How do you know you have all such matrices?

4. Give an example of a 3 x 3 matrix A such that neither A nor A² is the zero matrix, but A³ = 0. 5. Find all examples of matrices A which commute with both B = (6%) 0 and C = 00 0 (8 5) That is, find all matrices A so that AB = BA and AC = CA. How do you know you have all such matrices?

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 78E
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4. Give an example of a 3 x 3 matrix A such that neither A nor A² is the zero matrix, but A³ = 0. 5. Find all examples of matrices A which commute with both B = (6%) 0 and C = 00 0 (8 5) That is, find all matrices A so that AB = BA and AC = CA. How do you know you have all such matrices?
Transcribed Image Text:4. Give an example of a 3 x 3 matrix A such that neither A nor A² is the zero matrix, but A³ = 0. 5. Find all examples of matrices A which commute with both B = (6%) 0 and C = 00 0 (8 5) That is, find all matrices A so that AB = BA and AC = CA. How do you know you have all such matrices?
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