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 `lambd

Question

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 `lambd

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`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - 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`