Let λ∈R, the system of equations 2x1−4x2+λx3=1,x1−6x2+x3=2,λx1−10x2+4x3=3is consistent for

The system of equations are inconsistent, if the determinant of the coefficient matrix is zero and at least one  of Δ1, Δ2, Δ3 will be non zeroΔ=2−4λ1−61λ−104=0⇒2−24+10+44−λ+λ−10+6λ=0⇒−28+16−4λ−10λ+6λ2=0⇒6λ2−14λ−12=0⇒3λ2−7λ−6=0⇒λ−33λ+2=0⇒λ=3,−23Δ1=1−4λ2−613−104=10λ221324=10λ22−3320=10λ−10−3320=−2λ−3Δ2=21λ121λ34=25−14−λ+λ3−2λ=−2λ2+4λ+6Δ3=2−411−62λ−103=−2221132λ53=−22−1−23−2λ+15−3λobserving the above values, option 4 is correct answer