System of linear equations

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The value of K so that the system of equations $x + k y + 3 z = 0, 3 x + k y - 2 z = 0, 2 x + 3 y - 4 z = 0$ have non zero solution then

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Solution

$T h e c o n d i t i o n f o r a h o m o g e n e o u s s y s t e m t o h a v e a n o n - z e r o s o l u t i o n i s Δ = 0$
$\begin{array}{l} \Rightarrow |\begin{matrix} 1 & k & 3 \\ 3 & k & - 2 \\ 2 & 3 & - 4 \end{matrix}| = 0 \\ \Rightarrow 1 (- 4 k + 6) - k (- 12 + 4) + 3 (9 - 2 k) = 0 \\ \Rightarrow - 4 k + 6 + 8 k + 27 - 6 k = 0 \\ \Rightarrow - 2 k = - 33 \Rightarrow k = \frac{33}{2} \\ \Rightarrow k = 16.5 \end{array}$

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System of linear equations

Remember concepts with our Masterclasses.

The value of K so that the system of equations x+ky+3z=0,3x+ky−2z=0,2x+3y−4z=0have non zero solution then

The condition for a homogeneous system to have a non-zero solution is Δ=0⇒1k33k-223-4=0⇒1-4k+6-k-12+4+39-2k=0⇒-4k+6+8k+27-6k=0⇒-2k=-33⇒k=332⇒k=16.5

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The value of K so that the system of equations $x + k y + 3 z = 0, 3 x + k y - 2 z = 0, 2 x + 3 y - 4 z = 0$ have non zero solution then