Question

The system of equations x + ky + 3z = 0,

3x + ky –2z = 0, 2x + 3y – 4z = 0 possess a non-trivial

solution over the set of rationals, then 2k, is an integral element of the interval:

• A. [10, 20]
• B. (20, 30)
• C. [30, 40]
• D. (40, 50)

Answer 1

Answer: (C)

$30, 40$

Answer 2

For the given system to have a non-trivial solution, we must have

$\left| \begin{matrix} 1 & k & 3 \\ 3 & k & - 2 \\ 2 & 3 & - 4 \end{matrix} \right|$= 0 Ž k = $\frac{33}{2}$