Question

If the system of equation $x-ky-z=0,kx-y-z=0$ and $x+y-z=0$ has a non-zero solution, then $k$ is equal to

• A. $0,1$
• B. $1,-1$
• C. $-1,2$
• D. $2,-2$

Answer 1

The correct option is B $1,-1$

The given system of equation has a non-zero solution if $\left|A\right|=0$

For the given system of equations, we have

$A=\left|\begin{array}{ccc}1& -k& -1\\ k& -1& -1\\ 1& 1& -1\end{array}\right|$

Now $A=\left|\begin{array}{ccc}1& -k& -1\\ k& -1& -1\\ 1& 1& -1\end{array}\right|=0$

on solution gives

$\Rightarrow k^2=1\Rightarrow k=-1,1$