Question

The value of q, for which the following set of linear equations 2x + 3y = 0, 6x + qy = 0 can have non - trivial solution is

• A. 2
• B. 7
• C. 9
• D. 11

Answer 1

The correct option is C 9

AX = 0
$\Rightarrow \left[\begin{array}{cc}2& 3\\ 6& q\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}0\\ 0\end{array}\right]$
For non-trivial solution, $|A|=0\Rightarrow \left|\begin{array}{cc}2& 3\\ 6& q\end{array}\right|=0\Rightarrow q=9$