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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

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 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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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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