Find x such that the matrix is equal to its own inverse. A=begin{bmatrix}7 & x -8 & -7 end{bmatrix}

Tobias Ali 2020-11-03 Answered
Find x such that the matrix is equal to its own inverse.
A=[7x87]
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Expert Answer

Luvottoq
Answered 2020-11-04 Author has 95 answers

Step 1
Given matrix,
A=[7x87]
And,
A=A1
Formula for an inverse of a matrix is
A1=1detAadjA
Step 2 Now, det(A)=7(7)x(8)
det(A)=49+8x
det(A)=8x49
And,
adjA=[7x87]
so,
A1=[78x49x8x4988x4978x49]
Step 3
Now , as given
A=A1
[7x87]=[78x49x8x4988x4978x49]
on comparing the matrices,
7=78x49
7(8x49)=7
56x343=7
56x=3437
56x=3437
56x=336
x=33656
x=6
Step 4
Therefore,
The value of x such that the matrix is equal to its own inverse is
x=6

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Jeffrey Jordon
Answered 2022-01-29 Author has 2064 answers

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