Compute the product AB by the definition of the product of matrices, where Ab1 and...

Inyalan0

Inyalan0

Answered

2022-01-17

Compute the product AB by the definition of the product of matrices, where Ab1 and Ab2 are computed separately, and by the row-comumn rule for computing AB.
A=[233562],
B=[5114]
Set up the product Ab1, where b1 is the first column of B.
Ab1=?? where b1 is the first column of B.
Calculate Ab1 where b1 is the first column of of B.
Ab1=?
Set up the product Ab2 where b2 is the second column of B
Ab2=?
Calculate Ab2 where b2 is the second column of B.
Ab2=?
Determine the numerical expression for the first entry in the first column of AB using the​ row-column rule.

Answer & Explanation

porschomcl

porschomcl

Expert

2022-01-18Added 28 answers

We will use the product method of matrix to find solution to the problem.
Set up the product Ab1, where b, is the first column of B.
Ab1=2,5+3,1
=10+(3)
=103
=13
Calculate Ab1 where b1 is the first column of B
Ab1=13
Set up the product Ab2, where b1 is the second column of B.
Ab2=2,1+3,4
2+12
14
Calculate Ab2, where b2 is the second column of B.
Ab2=14
For the first entry,
((2)(5)+(3)(1)) is correct
Product AB=
[131410173214]
Archie Jones

Archie Jones

Expert

2022-01-19Added 34 answers

The calculation of Ab1 is as follows:
Ab1=
[223443][41]
=[2(4)+2(1)3(4)+4(1)4(4)+(3)(1)]
=[8212416+3]
[10819]
Therefore, Ab1= [10819]
The product Ab2= [223443][12]
The calculation of Ab1 is as follows:
Ab2=ZSK[223443][12]
=[2(1)+2(2)3(1)+4(2)4(1)+(3)(2)]
=[2+43+846]
=[6510]
Therefore, Ab2=ZSK[6510]
Write the matrix AB as
\[AB= [2(4)+2(1)2(1)+2(2)3(4)+4(1)3(1)+4(2)4(4)+(3)(1)4(1)+(3)(2)]\]
Thus, the first entry in the first column of the matrix AB is 2(4)+2(1).
Hence, the correct option is (C).
The final product of the matrices A and B is AB= [106851910]

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