The sum of distinct values of λ for which the system of equations : λ - 1 x + 3 λ + 1 y + 2 λ z = 0 λ - 1 x + 4 λ - 2 y + λ + 3 z = 0 2 x + 3 λ + 1 y + 3 λ - 1 z = 0 , Has non-zero solutions, is ....... .

Question

The sum of distinct values of λ for which the system of equations : λ - 1 x + 3 λ + 1 y + 2 λ z = 0 λ - 1 x + 4 λ - 2 y + λ + 3 z = 0 2 x + 3 λ + 1 y + 3 λ - 1 z = 0 , Has non-zero solutions, is ....... .,

MARKS App · Accepted Answer

λ - 1 3 λ + 1 2 λ λ - 1 4 λ - 2 λ + 3 2 3 λ + 1 3 ( λ - 1 ) = 0 R 2 → R 2 - R 1 R 3 → R 3 - R 1 λ - 1 3 λ + 1 2 λ 0 λ - 3 - λ + 3 3 - λ 0 λ - 3 = 0 C 1 → C 1 + C 3 3 λ - 1 3 λ + 1 2 λ 3 - λ λ - 3 3 - λ 0 0 λ - 3 = 0 ⇒ λ - 3 2 6 λ = 0 ⇒ λ = 0 , 3 sum of values of λ = 3

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