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

Answer 2

$\left| \begin{matrix} 1 & a & 0 \\ 0 & 1 & a \\ a & 0 & 1 \end{matrix} \right| = 0 \Rightarrow 1 + a(a)^{2} = 0$ $\Rightarrow$ $a^{3} = - 1 \Rightarrow a = - 1$