The set of all values of λ for which the system of linear equations 2x1 – 2x2 + x3 = λx1 2x1 – 3x2 + 2x3 = λx2 – x1 + 2x2 = λx3 has a non-trivial solution,

Engineering

Mathematics

Solving System of Linear Equation Cramers Rule

Question

The set of all values of λ for which the system of linear equations

2x₁ – 2x₂ + x₃ = λx₁

2x₁ – 3x₂ + 2x₃ = λx₂

– x₁ + 2x₂ = λx₃

has a non-trivial solution,

contains two elements

is an empty set

is a singleton

contains more than two elements

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$| \begin{matrix} 2 - λ & - 2 & 1 \\ 2 & - (3 + λ) & 2 \\ - 1 & 2 & - λ \end{matrix} | = 0 \Rightarrow λ = 1, - 3 .$