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Question
The value of λ for which the system of equations 2x−y−z=12,x−2y+z=−4,x+y+λx=4 has no solution is
The value of λ for which the system of equations 2x−y−z=12,x−2y+z=−4,x+y+λx=4 has no solution is
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Solution
The correct option is C −2
Given equations are 2x−y−z=12,x−2y+z=−4,x+y+λx=4The coefficient determinant
D=∣∣
∣∣2−1−11−2111λ∣∣
∣∣=−3λ−6
For no solution, the necessary condition is D=0.
Therefore, −3λ−6=0⇒λ=−2
It can be seen that for λ=−2, there is no solution for the given system or equations.
Given equations are 2x−y−z=12,x−2y+z=−4,x+y+λx=4
The coefficient determinant
D=∣∣ ∣∣2−1−11−2111λ∣∣ ∣∣=−3λ−6
For no solution, the necessary condition is D=0.
Therefore, −3λ−6=0
D=∣∣ ∣∣2−1−11−2111λ∣∣ ∣∣=−3λ−6
For no solution, the necessary condition is D=0.
Therefore, −3λ−6=0
⇒λ=−2
It can be seen that for λ=−2, there is no solution for the given system or equations.
It can be seen that for λ=−2, there is no solution for the given system or equations.
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