An ordered pair (a,b) for which the system of linear equations 1+ax+by+z=2,ax+1+by+z=3,ax+by+2z=2has a unique solution is

For unique solution of a non-homogeneous system of equations we must have Δ≠0. ⇒1+ab1a1+b1ab2≠0      apply R1⇒R1-R2,  R2⇒R2-R3 ⇒1-1001-1ab2≠0 ⇒12+b+10+a+0≠0 ⇒a+b+2≠0 ⇒Only 2,4 satisfies the condition.