Question

If $2ax-2y+3z=0,x+ay+2z=0\text{and}2x+az=0$ has a non-trivial solution,then the value of $a$ is:

• A. $1$
• B. $2$
• C. $4$
• D. $0$

Answer 1

The correct option is B $2$

For non-trivial solution, we must have
$\left|\begin{array}{ccc}2a& -2& 3\\ 1& a& 2\\ 2& 0& a\end{array}\right|=0$
$\Rightarrow 2a(a^2-0)+2(a-4)+3(0-2a)=0\Rightarrow 2a^3+2a-8+0-6a=0\Rightarrow 2a^3-4a-8=0\Rightarrow a^3-2a-4=0\Rightarrow (a-2)(a^2+2a+2)=0\Rightarrow a=2$