Let $\lambda \in $ R . The system of linear equations 2x1 - 4x2 + $\lambda $x3 = 1 x1 - 6x2 + x3 = 2 $\lambda $x1 - 10x2 + 4x3 = 3 is inconsistent for:

Question

Let $\lambda \in $ R . The system of linear equations
2x₁ - 4x₂ + $\lambda $x₃ = 1
x₁ - 6x₂ + x₃ = 2
$\lambda $x₁ - 10x₂ + 4x₃ = 3
is inconsistent for:

exactly one positive value of $\lambda $

exactly one negative value of $\lambda $

exactly two values of $\lambda $

every value of $\lambda $

Solution

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