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Question

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 solution is

A
(1,3)
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B
(3,1)
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C
(2,4)
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D
(4,2)
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Solution

The correct option is C (2,4)
For unique solution
Δ0∣ ∣1+αβ1α1+β1αβ2∣ ∣0
∣ ∣110011αβ2∣ ∣0α+β2

For Option C

α+β=2+4=6 which is 2

An ordered pair (2,4) for which the system of linear equations has a unique solution.

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