Question

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

• A. Zero
• B. 3
• C. 2
• D. 1

Answer 1

Answer: (C)

For non-trivial solution of given system of linear equations
$\begin{vmatrix}4&k&2\\ k&4&1\\ 2&2&1\end{vmatrix}=0$
$\Rightarrow 8+k(2-k)+2(2 k-8)=0$
$\Rightarrow -k^{2}+6 k-8=0$
$\Rightarrow k^{2}-6 k+8=0$
$\Rightarrow k=2,4$
Clearlv there exists two values of $k$