Question

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

• A. $-1$
• B. $1$
• C. $0$
• D. No real value

Answer 1

Answer: (A)

$-1$

For infinite number of solutions,

Determinant of coefficient matrix should vanish.

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

$\Rightarrow 1(1-0)-a(0-a^2)=0$, expand along 1st row

$\Rightarrow a^3+1=0\Rightarrow a=-1$ (only one real solutions)