Question

The system of equations ax + y + z = a –1, x + ay + z = a –1, x + y + az = a –1 has no solution, if a is

• A. –2
• B. both –2 and 1
• C. not –2
• D. 1

Answer 1

The correct option is A

–2

$△=\left|\begin{array}{ccc}a& 1& 1\\ 1& a& 1\\ 1& 1& a\end{array}\right|=0$
$\Rightarrow a=1or-2$
But $a\ne 1,$ at $a=1,x+y+z=0$ and equation has infinite solutions.
So choice (A) is correct.