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Let $λ$ be a real number for which the system of linear equations x+y+z=6, $4 x + λ y - λ z = λ - 2 and 3 x + 2 y - 4 z = - 5 has infinitely many solutions. Then λ is a root of the$ equation

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λ2−3λ−4=0

λ2+3λ−4=0

λ2−λ−6=0

λ2+λ−6=0

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detailed solution

Correct option is C

Given system has infinitely many solutions, Δ=0⇒1114λ-λ32-4=0 ⇒λ=3λ=3 satisfies the quadratic equation λ2-λ-6=0

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Let λ be a real number for which the system of linear equations x+y+z=6, 4x+λy-λz=λ-2 and 3x+2y-4z=-5 has infinitely many solutions. Then λ is a root of the equation

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Ready to Test Your Skills?

free study material

Let $λ$ be a real number for which the system of linear equations x+y+z=6, $4 x + λ y - λ z = λ - 2 and 3 x + 2 y - 4 z = - 5 has infinitely many solutions. Then λ is a root of the$ equation