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An ordered pair (alpha, beta) for which ...

An ordered pair `(alpha, beta)` for which the system of linear equations `(1+alpha)x+betay+z=2`, `alphax+(1+beta)y+z=3` and `alphax+betay+2z=2` has unique solution is: (a) (2,4) (b) (-3,1) (c) (-4,2) (d) (1,-3)

A

`(2,4)`

B

`(-4,2)`

C

`(1,-3)`

D

`(-3,1)`

Text Solution

Verified by Experts

The correct Answer is:
A
`|(1+alpha,beta,1),(alpha,1+beta,1),(alpha,beta,2)|ne0`
`R_(1)toR_(1)-R_(2) R_(2)to R_(2)-R_(3)`
`|(1,-1,0),(0,1,-1),(alpha,beta,2)|ne0`
`(2+beta)+1(0+alpha)ne0`
`2+beta+alphane0`
`alpha+betane -2`.
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