Mathematics - Determinant Question with Solution | TestHub

MathematicsDeterminantSystem of equationMedium2 minPYQ_2018

MathematicsMediumsingle choice

Let $S$ be the set of all real values of $k$ for which the system of linear equations
$x + y + z = 2$
$2 x + y - z = 3$
$3 x + 2 y + k z = 4$
has a unique solution. Then, $S$ is :

Options:

Answer:

Solution:

For unique solution, $∆ \neq 0$

$\Rightarrow |\begin{matrix} 1 & 1 & 1 \\ 2 & 1 & - 1 \\ 3 & 2 & k \end{matrix}| \neq 0$

$\Rightarrow 1 (k + 2) - 1 (2 k + 3) + 1 (4 - 3) \neq 0$

$\Rightarrow - k \neq 0 \Rightarrow k \neq 0$

Thus, $S = R - \{0\}$

Stream:JEESubject:MathematicsTopic:DeterminantSubtopic:System of equation

⏱ 2mℹ️ Source: PYQ_2018

Doubts & Discussion

Loading discussions...