Question

The number of non-trivial solutions of the system $x-y+z=0,x+2y-z=0,2x+y+3z=0$ is

• A. $0$
• B. $1$
• C. $2$
• D. infinite

Answer 1

The correct option is A $0$

For non-trivial solution we have $\Delta =0$
Here $\Delta =\left|\begin{array}{ccc}1& -1& 1\\ 1& 2& -1\\ 2& 1& 3\end{array}\right|$

$=1(6+1)+1(3+2)+1(1-4)$
$=7+5-3=9$
$\therefore \Delta \ne 0$
So, only trivial solution is possible.