Question

The system of equations $ax+4y+z=0,bx+3y+z=0,cx+2y+z=0$ has non-trivial solutions if $a,b,c$ are in

• A. $AP$
• B. $GP$
• C. $HP$
• D. none of these

Answer 1

The correct option is A $AP$

Here, $D=\left|\begin{array}{ccc}a& 4& 1\\ b& 3& 1\\ c& 2& 1\end{array}\right|$

For non-trivial solution, $D=0$

$\Rightarrow a-2b+c=0$

$\Rightarrow a+c=2b$

Hence, $a,b,c$ are in A.P.