The system of linear equations $\lambda x+2 y+2 z=5$ $2 \lambda x+3 y+5 z=8$ $4 x+\lambda y+6 z=10$ has:

(C) no solution when $\lambda=2$

(A) no solution when $\lambda=8$

(B) infinitely many solutions when $\lambda=2$

(D) a unique solution when $\lambda=-8$

JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Matrices

The system of linear equations

λ x + 2 y + 2 z = 5

2 λ x + 3 y + 5 z = 8

4 x + λ y + 6 z = 10

has:

Answer: (C)

The coefficient determinant is

D = λ 2 λ 4 23 λ 256 = (λ + 8) (2 - λ)

, which vanishes at

λ = 2

and

λ = - 8

. At

λ = 2

, replacing the first column by the constants gives

D_{1} = 5810232256 = 40 + 4 - 28 = 16 \neq = 0

. Since

D = 0

while

D_{1} \neq = 0

, the system is inconsistent, so it has no solution when

λ = 2

JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Single correct option