Question

For _______ value of $K\in (0,\frac{3}{2})$ does the following system of equation admits a non-trivial solution.

x + Ky + 3z = 0;
Kx + 2y + 2z = 0;
2x + 3y + 4z =0

• A. 1.25

Answer 1

The correct option is A 1.25
For given system of equations to have a non trivial solution,
$\left|\begin{array}{ccc}1& K& 3\\ K& 2& 2\\ 2& 3& 4\end{array}\right|=0$

1(8 - 6) - K (4K - 4) + 3(3K - 4) = 0

$\Rightarrow 4K^2-13K+10=0$
$\therefore K=2$
or K = 1.25