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Let the system of linear equations 4x + λy + 2z = 0 2x - y + z = 0 μx + 2y + 3z = 0, λ, μ ∈ R. has a non-trivial solution. Then which of the following is true ?

1. μ = 6, λ ∈ R
2. λ = 2, μ ∈ R
3. λ = 3, μ ∈ R
4. μ = -6, λ ∈ R

Correct answer: μ = -6, λ ∈ R

Solution

For the system to have a non-trivial solution, the determinant of the coefficient matrix must be zero. By substituting μ = -6 into the determinant calculation, it results in a condition that holds true, allowing λ to take any real value.

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