Question

If the system of equations

$x + 2y - 3z = 1,(k + 3)z = 3,(2k + 1)x + z = 0$is inconsistent,

then the value of k is

• A. –3
• B. $\frac{1}{2}$
• C. 0
• D. 2

Answer 1

Answer: (A)

–3

Answer 2

For the equations to be inconsistent $D = 0$

$\therefore$ $D = \left| \begin{matrix} 1 & 2 & - 3 \\ 0 & 0 & k + 3 \\ 2k + 1 & 0 & 1 \end{matrix} \right| = 0 \Rightarrow k = - 3$ and

$D_{1} = \left| \begin{matrix} 1 & 2 & - 3 \\ 3 & 0 & 0 \\ 0 & 0 & 1 \end{matrix} \right| \neq 0$, Hence system is inconsistent for

$k = - 3$