For non-trivial solution
∣42μλ−12213∣=0
⇒−20−6λ+λμ+8+2μ=0
⇒2μ−6λ+λμ=12
when μ=6,12−6λ+6λ=12
which is satisfied by all λ
When λ=2,4μ=24
When λ=3,5μ=30
When μ=−6,−12−6λ−6λ=12
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?
Held on 18 Mar 2021 · Verified 6 Jul 2026.
μ=6,λ∈R
λ=2,μ∈R
λ=3,μ∈R
μ=−6,λ∈R
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