The set of all values of \(\lambda\) for which the system of linear equations \(x-2 y-2 z=\lambda x\) \(x+2 y+z=\lambda y\) \(-x-y=\lambda z\)

(B) contains exactly two elements

(D) contains more than two elements

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Matrices

The set of all values of

λ

for which the system of linear equations

x - 2 y - 2 z = λ x

x + 2 y + z = λ y

- x - y = λ z

Answer: (A)

Written as a homogeneous system with

λ

on the diagonal, a non-trivial solution needs the coefficient determinant to vanish. Evaluating that determinant gives

(λ - 1)^{3} = 0

, so

λ = 1

is the only value and the set of admissible

λ

is the singleton

{1}

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Single correct option