Determine those values of for which the following set of, Engineering Mathematics

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Determine those values of for which the following set of

Question: 1. Solve the following set of equations using matrix methods.

x₁ + 2x₂ + 2x₃ = 1

2x₁ + 2x₂ + 3x₃ = 3

x₁ - x₂ + 3x₃ = 5

2. Determine those values of λ for which the following set of equations may possess a nontrivial solution.

3x₁ + x₂ - λx₃ = 0

4x₁ - 2x₂ - 3x₃ = 0

2λx₁ + 4x₂ + λx₃ = 0

For each permissible value of λ, determine the most general solution.

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