QJEEM22Ma5d87: JEE Main 2022 Mathematics - Class 12 JEEM22Ma5d87 Solution: The system of equations is consistent for all k in the set

Question

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The system of equations

$- kx + 3y - 14z = 25$

$- 15x + 4y - kz = 3$

$- 4x + y + 3z = 4$

is consistent for all k in the set

Accepted Answer

The system may be inconsistent if

$| \begin{matrix} - k & 3 & - 14 \\ - 15 & 4 & - k \\ - 4 & 1 & 3 \end{matrix} | = 0 \Rightarrow k = \pm 11$

Hence if system is consistent then $k \in R - \{ 11, - 11\}$ .

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