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Question

The value of k for which, the system of equations
kx + 3y - z = 1; x + 2y + z = 2 and -kx + y + 2z = -1 have no solution, is .

A
k = -7
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B
k = 7
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C
k=72
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D
k=72
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Solution

The correct option is C k=72
The given system of equations will have no solution if:
D=k31121k12∣ ∣=0k(41)3(2+k)1(1+2k)=02k7=0k=72For, k=72,D1=131221112∣ ∣=160Hence, D=0 and D10. So, the given system of equations will have no solution for k=72

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