Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If the system of equations λ x 1 + x 2 + x 3 = 1, x 1 + λ x 2 + x 3 = 1, x 1 + x 2 + λ x 3 = 1 is consistent, then λ can be-
Text Solution
Verified by ExpertsThe correct answer is:
D
Let Δ = 
= 
[C 1 → C 1 + C 2 + C 3 ]
= ( λ + 2) 
= ( λ + 2) 
= ( λ + 2) ( λ – 1) 2 [using C 2 → C 2 – C 1 and C 3 → C 3 – C 1 ]
If Δ = 0, then λ = –2 or λ = 1. But when λ = 1, the system of equation becomes x 1 + x 2 + x 3 = 1 which has infinite number of solutions. When λ = – 2, by adding three equations, we obtain 0 = 3 and thus, the system of equations is inconsistent.
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