x + k y − z = 0 , 3 x − k y − z = 0 and x − 3 y + z = 0 has non-zero solution for k = Options: A . &nbsp-1 B . &nbsp0 C . &nbsp1 D . &nbsp2

Answer: Option C : C It has a non-zero solution if ∣ ∣ ∣ ∣ 1 k − 1 3 − k − 1 1 − 3 1 ∣ ∣ ∣ ∣ = 0 ⇒ − 6 k + 6 = 0 ⇒ k = 1 .

x + ky − z = 0, 3x −

Question

x + k y - z = 0, 3 x - k y - z = 0

and

x - 3 y + z = 0

has non-zero solution for k =

Options:

A . -1

B . 0

C . 1

D . 2

Answer: Option C
:
C
It has a non-zero solution if

∣ ∣∣ ∣ \begin{matrix} 1 & k & - 1 3 & - k & - 1 1 & - 3 & 1 \end{matrix} ∣ ∣∣ ∣ = 0 \Rightarrow - 6 k + 6 = 0 \Rightarrow k = 1 .

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