Investigate for what values of λ , μ the simultaneous equations
x + y + z = 6; x + 2 y + 3 z = 10 & x + 2 y + λ z = μ have;
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
λ ≠ 3 λ = 3, μ = 10 λ = 3, μ ≠ 10
Sol. Δ = 
= λ –3 ; Δ x = 
= 2 λ + µ – 16
Δ y = 
= 4 λ – 2µ + 8 ; Δ z = 
= (µ – 10)
(i) For unique solution Δ ≠ 0 ∴ λ ≠ 3
(ii) For infinite no. of solution Δ = 0, Δ x = 0, Δ y = 0, Δ z = 0.
∴ λ = 3, µ = 10
(iii) For no. solution Δ = 0, & at least are of Δ x , Δ y , Δ z is non-zero.
∴ λ = 3, µ ≠ 10
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