Step 6. As seen in Steps 4 and 5, it takes some very special conditions, indeed, for two matrices to commute. Make up one more size 3 x 3 example. Be sure your example is different from that given in Step 4. In other words, provide two matrices A and B such that AB BA. But, this time, make sure your matrices A and B are not diogonal In the table below, enter your matrices A and B and verify that their products AB and BA are the same. Simplify your results as much as possible. A AB B BA Step 7. For this final step, let M be the set of all matrices and let D be the subset consisting of all 3 x 3 diagonal matrices. Conclusion. From the results of this and previous exercises, we have found that the set D commutative under matrix multiplication because AB = BA for matrices A and B in D By contrast, note that M commutative because AB = BA for matrices A and B in M. So, while Mis not there exist subsets of M which are. And, D is just one example: can you think of others?
Step 6. As seen in Steps 4 and 5, it takes some very special conditions, indeed, for two matrices to commute. Make up one more size 3 x 3 example. Be sure your example is different from that given in Step 4. In other words, provide two matrices A and B such that AB BA. But, this time, make sure your matrices A and B are not diogonal In the table below, enter your matrices A and B and verify that their products AB and BA are the same. Simplify your results as much as possible. A AB B BA Step 7. For this final step, let M be the set of all matrices and let D be the subset consisting of all 3 x 3 diagonal matrices. Conclusion. From the results of this and previous exercises, we have found that the set D commutative under matrix multiplication because AB = BA for matrices A and B in D By contrast, note that M commutative because AB = BA for matrices A and B in M. So, while Mis not there exist subsets of M which are. And, D is just one example: can you think of others?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Step 6. As seen in Steps 4 and 5, it takes some very special conditions, indeed, for two matrices to commute.
Make up one more size 3 x 3 example. Be sure your example is different from that given in Step 4. In other
words, provide two matrices A and B such that AB= BA. But, this time, make sure your matrices A and
B are not diagonal. In the table below, enter your matrices A and B and verify that their products AB
and BA are the same. Simplify your results as much as possible.
A
B
АВ
B
BA
Step 7. For this final step, let M be the set of all matrices and let D be the subset consisting of all 3 x 3
diagonal matrices.
Conclusion. From the results of this and previous exercises, we have found that the set D
commutative under matrix multiplication because AB = BA for
matrices A and B in D By contrast, note that M
commutative because
AB = BA for
matrices A and B in M. So, while M is not
there exist subsets of M which are. And, D is just one example: can you think of others?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79770301-0c06-4a6d-bc73-b33747389ebd%2Fcb948f49-9789-4229-b6c6-d5a3247d6e63%2F4h0cjeh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Step 6. As seen in Steps 4 and 5, it takes some very special conditions, indeed, for two matrices to commute.
Make up one more size 3 x 3 example. Be sure your example is different from that given in Step 4. In other
words, provide two matrices A and B such that AB= BA. But, this time, make sure your matrices A and
B are not diagonal. In the table below, enter your matrices A and B and verify that their products AB
and BA are the same. Simplify your results as much as possible.
A
B
АВ
B
BA
Step 7. For this final step, let M be the set of all matrices and let D be the subset consisting of all 3 x 3
diagonal matrices.
Conclusion. From the results of this and previous exercises, we have found that the set D
commutative under matrix multiplication because AB = BA for
matrices A and B in D By contrast, note that M
commutative because
AB = BA for
matrices A and B in M. So, while M is not
there exist subsets of M which are. And, D is just one example: can you think of others?
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