Question

If the system of equations $x+ay=0$, $az+y=0$ and $ax+z=0$ has infinite solutions, then the value of $a$ is

• A. $-1$
• B. $1$
• C. $0$
• D. no real values

Answer 1

Answer: (A)

$-1$

Given equation $x+ay=0,az+y=0,ax+z=0$ has infinite solution

$\therefore \left|\begin{array}{ccc}1& a& 0\\ 0& 1& a\\ a& 0& 1\end{array}\right|=0$

$\Rightarrow 1(1-0)-a(0-a^2)+0=0$

$\Rightarrow 1+a^3=0$

$\Rightarrow a=-1$