An ordered pair (α,β) for which the system of linear equations (1+α)x+βy+z=2,αx+(1+β)y+z=3, αx+βy+2z=2 has a unique solutions, is

An ordered pair (α,β) for which the system of linear equations (1+α)x+βy+z=2,αx+(1+β)y+z=3αx+βy+2z=2 has a unique solutions, is

  1. A

    (3,1)

  2. B

    (2,4)

  3. C

    (1,-3)

  4. D

    (-4,2)

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    Solution:

    For unique solution

     1+αβ1α1+β1αβ20(1+α)(2+2ββ)β(2αα)+1(αβααβ)02+2ββ+2α+2αβαβ2αβ+αβα02+α+β0

     (2,4) satisfies the above condition.

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