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Question

Consider the system of equations x+y+z=6,x+2y+3z=10,x+2y+λz=μ
The system has infinite solutions if:

A
λ3
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B
λ=3,μ=10
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C
λ=3,μ10
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D
none of these
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Solution

The correct option is B λ=3,μ=10
Given system of equations AX=B
where A=11112312λ, X=xyz,B=610μ
For infinitely many solution,
D=0
∣ ∣11112312λ∣ ∣=0
2(λ3)(λ3)=0
λ=3
Also, D1=∣ ∣6111023μ23∣ ∣=0
μ=10
D2=∣ ∣16111031μ3∣ ∣=0
μ=10
D3=∣ ∣116121012μ∣ ∣=0
μ=10

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