Step 1. Dimension Analysis Observe that the two given matrices are the same size. Namely, the matrices A and B each have dimensions: Consequentlų, their products AB and BA also each have the same size. Namely, the products AB and BA each have the dimensions: Step 2. Calculate the matrix product AB and enter your results into the table below. Simplify your result as much as possible. If the answer is undefined, leave the answer blank.or type the letter.N AB -4 12 12 -13 6 -6 -14 -6 3. -1

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Step 3. Calculate the matrix product BA and enter your results into the table below. Simplify your result
as much as possible. If the answer is undefined, leave the answer blank or type the letter: N
B
ВА
12
13
4
1
12
8
1
-6 -14
-1
5
3
Step 4. Recall the definition of commutativity. Then, based on your observations from Steps 1 through 3
above, determine whether or not matrix multiplication is commutative.
Definition. A set of objectsS is commutative under multiplication if
elements A and
B in S. it is true that:
Observation, Even the set M of all square n xn matrices is not
under matrix
multiplication. For example, in Steps1 through 3 cbove, we have two matrices A and B in M.
where the corresponding entries of the two products AB and BA
all equal, even
though AB and BA are both the same size.
Transcribed Image Text:Step 3. Calculate the matrix product BA and enter your results into the table below. Simplify your result as much as possible. If the answer is undefined, leave the answer blank or type the letter: N B ВА 12 13 4 1 12 8 1 -6 -14 -1 5 3 Step 4. Recall the definition of commutativity. Then, based on your observations from Steps 1 through 3 above, determine whether or not matrix multiplication is commutative. Definition. A set of objectsS is commutative under multiplication if elements A and B in S. it is true that: Observation, Even the set M of all square n xn matrices is not under matrix multiplication. For example, in Steps1 through 3 cbove, we have two matrices A and B in M. where the corresponding entries of the two products AB and BA all equal, even though AB and BA are both the same size.
Step 1. Dimension Analysis
Observe that the two given matrices are the same size. Namelų, the matrices A and B each have
dimensions:
Consequently, their products AB and BA also each have the same size. Namely, the products
AB and BA each have the dimensions:
Step 2. Calculate the matrix product AB and enter your results into the table below. Simplifų your result
as much as possible. If the answer is undefined, leave the answer blank.or type the letter:N
В
АВ
-4
1
12
12
-13
6.
-14
8.
0.
3
7.
- 1
Transcribed Image Text:Step 1. Dimension Analysis Observe that the two given matrices are the same size. Namelų, the matrices A and B each have dimensions: Consequently, their products AB and BA also each have the same size. Namely, the products AB and BA each have the dimensions: Step 2. Calculate the matrix product AB and enter your results into the table below. Simplifų your result as much as possible. If the answer is undefined, leave the answer blank.or type the letter:N В АВ -4 1 12 12 -13 6. -14 8. 0. 3 7. - 1
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