JEE MAIN - Mathematics (2022 - 25th June Evening Shift - No. 4)

The system of equations

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

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

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

is consistent for all k in the set

R $$-$$ {$$-$$11, 13}

R $$-$$ {13}

R $$-$$ {$$-$$11, 11}

The system may be inconsistent if

$$\left| {\matrix{ { - k} & 3 & { - 14} \cr { - 15} & 4 & { - k} \cr { - 4} & 1 & 3 \cr } } \right| = 0 \Rightarrow k = \, \pm \,11$$

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