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Question: \(x + ky - z = 0,3x - ky - z = 0\)and \(x - 3y + z = 0\) has non-zero solution for k =...

x+ky−z=0,3x−ky−z=0x + ky - z = 0,3x - ky - z = 0and x−3y+z=0x - 3y + z = 0 has non-zero solution for k =

A

– 1

B

0

C

1

D

2

Answer

1

Explanation

Solution

It has a non-zero solution if

∣1k−13−k−11−31∣\left| \begin{matrix} 1 & k & - 1 \\ 3 & - k & - 1 \\ 1 & - 3 & 1 \end{matrix} \right|=0 ⇒−6k+6=0⇒k=1\Rightarrow - 6k + 6 = 0 \Rightarrow k = 1.