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The value of lamda so that the matric A^...

The value of `lamda` so that the matric `A^(-1)lamdaI` is singular where `A=[{:(6,-2,2),(-2,3,-1),(2,-1,3):}]`

A

`(1)/(2),(-1)/(2)`

B

`1,(-1)/(2)`

C

`1,(1)/(8)`

D

`(1)/(2),(1)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
D
`|A^(-1)-lamdal|=0`
`|A||A^(-1)-lamdal|=0`
`|l-lamdaA|=0`
`|(l)/(lamda)-A|=0`
`|A-(1)/(lamda)l|=0`
`|{:(6-(1)/(lamda),-2,2),(-2,3-(1)/(lamda),-1),(2,-1,3-(1)/(lamda)):}|=0`
`lamda=(1)/(2),(1)/(8)`
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