Question

The value of k for which the set of equations $x + ky + 3z = 0,3x + ky - 2z = 0,2x + 3y - 4z = 0$has a non trivial solution over the set of rationals is.

• A. 15
• B. 31/2
• C. 16
• D. 33/2

Answer 1

Answer: (D)

33/2

Answer 2

Given set of equations will have a non trivial solution if the determinant of coefficient of x, y, z is zero

i.e., $\left| \begin{matrix} 1 & k & 3 \\ 3 & k & - 2 \\ 2 & 3 & - 4 \end{matrix} \right| = 0 \Rightarrow 2k - 33 = 0$ or $k = \frac{33}{2}$.