Mathematics | VITEEE 2014 | Discussion Page

If the system of equations $x+ky-z=0$ , $3x-ky-z=0$ and $x-3y+z=0$ has non-zero solution , the k is equal to

A) -1

B) 0

C) 1

D) 2

Option C

The system has non-zero solution. if

$\begin{bmatrix}1 & k&-1 \\3 & -k&-1\\1&-3&1 \end{bmatrix}=0$

$\Rightarrow$ 1(-k-3)-k(3+1)-1(-9+k)=0

$\Rightarrow$ -6k+k=0

$\Rightarrow$ k=1

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