First slide

System of linear equations

Question

The sum of values of ‘k’ for which the linear equations $4 x + k y + 2 z = 0, k x + 4 y + z = 0, 2 x + 2 y + z = 0$ possess a non-zero solution is

Easy

A

2
B

5
C

6
D

1

Solution

$T h e s y s t e m o f e q u a t i o n s h a s a n o n - z e r o s o l u t i o n \Rightarrow Δ = 0$
$\Rightarrow |\begin{matrix} 4 & k & 2 \\ k & 4 & 1 \\ 2 & 2 & 1 \end{matrix}| = 0 \Rightarrow 4 (4 - 2) - k (k - 2) + 2 (2 k - 8) = 0 \Rightarrow k^{2} - 6 k + 8 = 0$
$\Rightarrow k = 2, 4$
$∴$ Sum = 4+2 = 6

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