Question

The value of $a$ for which the system of equations $ax+y+z=0$, $x+ay+z=0$, $x+y+z=0$, possess non-zero solutions are given by

• A. $1,2$
• B. $1,-1$
• C. $1$
• D. None of these

Answer 1

The correct option is C $1$

The given equations are $ax+y+z=0,x+ay+z=0,x+y+z=0$

So we have $\Rightarrow A=\left[\begin{array}{ccc}a& 1& 1\\ 1& a& 1\\ 1& 1& 1\end{array}\right]$

Now for non-zero solutions, $A=0$

So solving for the matrix we get,

$a(a-1)-1(1-1)+(1-a)=a^2-2a+1={(a-1)}^2=0$

So $a=1$