Question

The number of values of k for which the linear equations
$4x+ky+2z=0$
$kx+4y+z=0$
$2x+2y+z=0$
possess a non-zero solution is : ?

• A. 3
• B. 2
• C. 1
• D. 0

Answer 1

The correct option is B 2

Here $D=\left|\begin{array}{ccc}4& k& 2\\ k& 4& 1\\ 2& 2& 1\end{array}\right|$
For non-zero solution
$D=0$

On expanding the above determinant we get,
$\Rightarrow k^2-6k+8=0$
$\Rightarrow k=2,4$
Therefore, there are 2 values of $k$ for non-zero solutions.
Hence, option 'B' is correct.