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If A=[{:(8,-6,2),(-6,7,-4),(2,-4,3):}] a...

If `A=[{:(8,-6,2),(-6,7,-4),(2,-4,3):}]` and `X` is a non zero column matrix such that `AX=lambdaX`, where `lambda` is a scalar, then values of `lambda` can be

A

`3`

B

`6`

C

`12`

D

`15`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`(a,d)` Let `X=[{:(a),(b),(c):}]`
`:.AX=lambdaXimplies[{:(8,-6,2),(-6,7,-4),(2,-4,3):}][{:(a),(b),(c ):}]=[{:(lambdaa),(lambdab),(lambdac ):}]`
`implies(8-lambda)a-6b+2c=0`
`-6a+(7-lambda)b-4c=0`
and `2a-4b+(3-lambda)c=0`
For non zero solution `[{:(8-lambda,,-6,,2),(-6,,7-lambda,,-4),(2,,-4,,3-lambda):}]=0`
`implieslambda=0,3,15`
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