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Let {:A=[(1,2),(-5,1)]and A^(-1)=xA+yI:}...

Let `{:A=[(1,2),(-5,1)]and A^(-1)=xA+yI:}`, then the values of x and y are

A

`x=(-1)/11,y=2/11`

B

`x=(-1)/11,y=(-2)/11`

C

`x=1/11,y=2/11`

D

`x=1/11,y=(-2)/11`

Text Solution

Verified by Experts

The correct Answer is:
A
`A^(-1)=(adj(A))/(|A|)=1/(1+10)[(1,-2),(5,1)]=1/11[(1,-2),(5,1)]`
Also `A^(-1)=xA+yl`
`implies1/11[(1,-2),(5,1)]=[(x,2x),(-5x,x)]+[(y,0),(0,y)]`
`impliesx+y=1/11, 2x=(-2)/11`
`impliesx=(-1)/11,y=2/11`
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