The set of all values of λ for which the system of linear equations: 2 x 1 - 2 x 2 + x 3 = λ x 1 2 x 1 - 3 x 2 + 2 x 3 = λ x 2 - x 1 + 2 x 2 = λ x 3 has a non-trivial solution,

Question

The set of all values of λ for which the system of linear equations: 2 x 1 - 2 x 2 + x 3 = λ x 1 2 x 1 - 3 x 2 + 2 x 3 = λ x 2 - x 1 + 2 x 2 = λ x 3 has a non-trivial solution,, Contains more than two elements., Is an empty set., Is a singleton., Contains two elements.

MARKS App · Accepted Answer

2 - λ x 1 - 2 x 2 + x 3 = 0 2 x 1 - λ + 3 x 2 + 2 x 3 = 0 - x 1 + 2 x 2 - λ x 3 = 0 The systems of linear equations will have a non-trivial solution ⇒ 2 - λ - 2 1 2 - λ - 3 2 - 1 2 - λ = 0 ⇒ 2 - λ λ 2 + 3 λ - 4 + 2 - 2 λ + 2 + 1 4 - λ - 3 = 0 2 λ 2 + 6 λ - 8 - λ 3 - 3 λ 2 + 4 λ - 4 λ + 4 + 1 - λ = 0 - λ 3 - λ 2 + 5 λ - 3 = 0 λ 3 + λ 2 - 5 λ + 3 = 0 λ - 1 λ 2 + 2 λ - 3 = 0 λ - 1 λ + 3 λ - 1 = 0 ⇒ λ = -3 , 1 , 1

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