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Question

The system of equations
kx+(k+1)y+(kāˆ’1)z=0
(k+1)x+ky+(k+2)z=0
(kāˆ’1)x+(k+2)y+kz=0 has a non-trivial solution for

A
Exactly three values of k
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B
Exactly two real values of k
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C
Exactly one real value of k
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D
Infinite real values of k
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Solution

The correct option is C Exactly one real value of k
For non-trivial solution

∣ ∣kk+1k1k+1kk+2k1k+2k∣ ∣=0
R2R2R1, R3R3R1
∣ ∣kk+1k1113111∣ ∣=0k=12

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