Question

An ordered pair (α,β) for which the system of linear equations (1+α)x+βy+z=2αx+(1+β)y+z=3αx+βy+2z=2 has a unique solution, is:(1,−3)(−3,1)(−4,2)(2,4)

Solution

The correct option is D (2,4)The system of linear equation are (1+α)x+βy+z=2αx+(1+β)y+z=3αx+βy+2z=2 for unique solution, Δ≠0 ⇒∣∣ ∣∣1+αβ1α1+β1αβ2∣∣ ∣∣≠0 Apply R1→R1−R2 ⇒∣∣ ∣∣1−10α1+β1αβ2∣∣ ∣∣≠0 ⇒1(2+2β−β)+1(2α−α)+0 ≠0⇒α+β+2 ≠0⇒α+β≠−2 Hence, (2,4) will satisfy this condition.

Suggest corrections