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If A=[(x,-2),(3,7)] and A^(-1)=[(7/34,1/...

If `A=[(x,-2),(3,7)]` and `A^(-1)=[(7/34,1/17),((-3)/34,2/17)]`,then the value of x is

A

2

B

3

C

-4

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
Given `a=[(x,-2),(3,7)]`
Now `|A|=|(x,-2),(3,7)|=7x+6`
`:.A^(-1)=(adj(A))/(|A|)=1/(7x+6)[(7,2),(-3,x)]`
But, given `A^(-1)=[(7/34, 1/17),((-3)/34,2/17)]`
`:.7/(7x+6)=7/34implies7x+6=34`
`implies7x=28impliesx=4`
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