Determine whether the statement, (A + B)^{-1} = A^{-1}+B^{-1}, assuming A, B, and A + B are invertible, is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

boitshupoO

boitshupoO

Answered question

2021-03-02

Determine whether the statement, (A+B)1=A1+B1, assuming A, B, and A + B are invertible, is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

Answer & Explanation

unett

unett

Skilled2021-03-03Added 119 answers

Step 1
Given:
(A+B)1=A1+B1
To determine:
If A, B and (A+B) are invertible matrices then to check if the statement is True or False: Solution:The given statement is false as the given statement is not valid for all the invertible matrices:
Therefore, We can prove this using an example:
Step 2
Lets
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-24Added 2605 answers

Answer is given below (on video)

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