Mathematics - Determinant Question with Solution | TestHub

MathematicsDeterminantSystem of equationMedium2 minPYQ_2019

MathematicsMediumsingle choice

The system of linear equations
$x + y + z = 2$
$2 x + 3 y + 2 z = 5$
$2 x + 3 y + (a^{2} - 1) z = a + 1$

Options:

Answer:

Solution:

Here, $D = |\begin{matrix} 1 & 1 & 1 \\ 2 & 3 & 2 \\ 2 & 3 & a^{2} - 1 \end{matrix}|$

$= a^{2} - 3$

Hence at $| a | = \sqrt{3}$ , $D = 0$ . So system don't have unique solution.

At $a = 4$ , $D \neq 0$ , So, system has unique solution. Hence not inconsistent.

At $| a | = \sqrt{3}, D = 0$ and $2^{n d}$ & $3^{r d}$ equation are parallel. Hence no solution are possible.

Hence, system is inconsistent for $| a | = \sqrt{3}$

Stream:JEESubject:MathematicsTopic:DeterminantSubtopic:System of equation

⏱ 2mℹ️ Source: PYQ_2019

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