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

Question

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, no solution when λ = 8, a unique solution when λ = - 8, no solution when λ = 2, infinitely many solutions when λ = 2

MARKS App · Accepted Answer

∆ = λ 2 2 2 λ 3 5 4 λ 6 = λ 18 - 5 λ - 2 12 λ - 20 + 2 2 λ 2 - 12 = - λ 2 - 6 λ + 16 = λ + 8 2 - λ ∆ = 0 for λ = 2 , ∆ 1 = 5 2 2 8 3 5 10 2 6 ∆ 1 = 5 18 - 10 - 2 48 - 50 + 2 16 - 30 ∆ 1 = 40 + 4 - 28 ≠ 0 No solution for λ = 2 .

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