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В 3 0. -2 12 15 10 -7 2 -3 0 15 0. 12 0 10 anglusis (on ugur own pgper), and determine the

В 3 0. -2 12 15 10 -7 2 -3 0 15 0. 12 0 10 anglusis (on ugur own pgper), and determine the

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.1: Algebra Of 2 X 2 Matrices
Problem 44PS
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+ Algoma University Step 5. Perform a dimension analysis (on your own paper), and determine the general dimension requirements that are necessary so that two matrices A and B could possibly commute. Statement 4 If AB= BA, then the matrices A and B must both be as well as In other words, without these dimension requirements, it is not possible for AB to equal BA, because even if the products are defined their respective sizes will not match. Observe that, while Statements 4 provides the necessary conditions for two matrices A and B commute, these conditions are not sufficient. In previous exercises, we have seen examples of matrices which satisfy both conditions and yet we still get AB BA commute
Transcribed Image Text:+ Algoma University Step 5. Perform a dimension analysis (on your own paper), and determine the general dimension requirements that are necessary so that two matrices A and B could possibly commute. Statement 4 If AB= BA, then the matrices A and B must both be as well as In other words, without these dimension requirements, it is not possible for AB to equal BA, because even if the products are defined their respective sizes will not match. Observe that, while Statements 4 provides the necessary conditions for two matrices A and B commute, these conditions are not sufficient. In previous exercises, we have seen examples of matrices which satisfy both conditions and yet we still get AB BA commute
Step 4. Here is an easy example illustrating the veracity of Statement 3. In the the following problem, A and B are each diagonal matrices: the only nonzero entries are on the main diagonal. Calculate the matrix products AB and BA and enter your results into the tables below. Verify that the matrices A and B do commute. So, for this special example, it is true that: AB= BA %3D В АВ 3 0. -2 12 0. 15 0. 10 -7 B A BA -2 3 15 0. 12 -7 10 Step 5 anal (on your own paper), and determine the general dimension
Transcribed Image Text:Step 4. Here is an easy example illustrating the veracity of Statement 3. In the the following problem, A and B are each diagonal matrices: the only nonzero entries are on the main diagonal. Calculate the matrix products AB and BA and enter your results into the tables below. Verify that the matrices A and B do commute. So, for this special example, it is true that: AB= BA %3D В АВ 3 0. -2 12 0. 15 0. 10 -7 B A BA -2 3 15 0. 12 -7 10 Step 5 anal (on your own paper), and determine the general dimension
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