Mathematics - Determinant Question with Solution | TestHub

MathematicsDeterminantSystem of equationEasy2 minPYQ_2022

MathematicsEasysingle choice

The system of equations
$- k x + 3 y - 14 z = 25$

$- 15 x + 4 y - k z = 3$

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

Question: is consistent for all $k$ in the set

Answer:

Solution:

For consistent solutions $∆ \neq 0$

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

$\Rightarrow - k (12 + k) - 3 (- 45 - 4 k) - 14 (- 15 + 16) \neq 0$

$\Rightarrow - 12 k - k^{2} + 135 + 12 k - 14 \neq 0$

$\Rightarrow k^{2} \neq 121$

$\Rightarrow k \neq 11, - 11$

Stream:JEESubject:MathematicsTopic:DeterminantSubtopic:System of equation

⏱ 2mℹ️ Source: PYQ_2022

Loading discussions...