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Mathematics - Determinant Question with Solution | TestHub

MathematicsDeterminantSystem of equationEasy2 minPYQ_2022

MathematicsEasysingle choice

If the system of linear equations
$2 x + y - z = 7$
$x - 3 y + 2 z = 1$
$x + 4 y + δ z = k$ , where $δ, k \in R$
has infinitely many solutions, then $δ + k$ is equal to

Options:

Answer:

B

Solution:

For infinitely many solutions, $∆ = |\begin{matrix} 2 & 1 & - 1 \\ 1 & - 3 & 2 \\ 1 & 4 & δ \end{matrix}| = 0$

$\Rightarrow δ = - 3$

and $∆_{1} = |\begin{array}{ccr} 7 & 1 & - 1 \\ 1 & - 3 & 2 \\ K & 4 & - 3 \end{array}| = 0 \Rightarrow k = 6$

$\Rightarrow δ + K = 3$

Stream:JEESubject:MathematicsTopic:DeterminantSubtopic:System of equation

⏱ 2mℹ️ Source: PYQ_2022

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