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Question

The value of λ for which the system of equations 2xyz=12,x2y+z=4,x+y+λx=4 has no solution is

A
3
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B
3
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C
2
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D
2
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Solution

The correct option is C 2
Given equations are 2xyz=12,x2y+z=4,x+y+λx=4
The coefficient determinant
D=∣ ∣21112111λ∣ ∣=3λ6
For no solution, the necessary condition is D=0.
Therefore, 3λ6=0
λ=2
It can be seen that for λ=2, there is no solution for the given system or equations.

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