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If system of linear equations x+y+z=6,x+2y+3z=14,2x+5y+λz=μ(λ,μR) has a unique solution, then

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a
λ≠8
b
λ=8,μ≠36
c
λ=8,μ=36
d
λ=8,μ=26

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detailed solution

Correct option is A

Augmented Matrix =11161231425λμApply :R2→R2−R1 ; R3→R3−2R1                                       ~1116012803λ−2μ−12Apply:R3→R3−3R2                                       ~1116012800λ−8μ−36Since the system has unique solution⇒ λ−8≠0 ⇒ λ≠8


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