Explain why the formula is not valid for matrices. Illustrate your argument with examples. (A+B)(A+B)=A^2+2AB+B^2

Harlen Pritchard 2020-11-26 Answered
Explain why the formula is not valid for matrices. Illustrate your argument with examples.
(A+B)(A+B)=A2+2AB+B2
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Expert Answer

SchulzD
Answered 2020-11-27 Author has 83 answers
Step 1
Consider the provided question,
According to you we have to solve only 38 question.
(38)
Show that why the formula (A+B)(A+B)=A2+2AB+B2 is not valid for matrices. In the case of matrices,
(A+B)(A+B)=AA+AB+BA+BB
=A2+AB+BA+B2
Since, we know that hhe relation AB=BA is not always correct.
Step 2
Now, consider an example.
Let A=[1203] and B=[0112]
AB=[1203][0112]
=[10+211(1)+2200+310(1)+32]
=[2336]
Step 3
A=[1203] and B=[0112]
BA=[0112][1203]
=[01+(1)002+(1)311+2012+23]
=[0318]
Here, ABBA
and as a result AB+BA2AB
Thus, the formula (A+B)(A+B)=A2+2AB+B2 is not correct for all matrices.
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Jeffrey Jordon
Answered 2022-01-22 Author has 2064 answers

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