System of linear equations

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Question

If the system of equations $x + k y + 3 z = 0,$ $k x + 2 y + 2 z = 0,$ $2 x + 3 y + 4 z = 0$ admits of non-trivial solution, then sum of values of $' k'$

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Solution

The system has a non-trivial solution $\Rightarrow Δ = 0$
$\begin{array}{l} \Rightarrow |\begin{array}{l} 1 & k & 3 \\ k & 2 & 2 \\ 2 & 3 & 4 \end{array}| = 0 \\ \Rightarrow 1 (8 - 6) - k (4 k - 4) + 3 (3 k - 4) = 0 \\ \Rightarrow 4 k^{2} - 13 k + 10 = 0 \\ \Rightarrow k = 2, 5 / 4 \end{array}$
$∴ Sum of values of K = 2 + \frac{5}{4} = \frac{13}{4} = 3.25$

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System of linear equations

Remember concepts with our Masterclasses.

If the system of equations x+ky+3z=0,kx+2y+2z=0,2x+3y+4z=0admits of non-trivial solution, then sum of values of'k'

The system has a non-trivial solution ⇒Δ=0⇒1k3k22234=0⇒1(8-6)-k(4k-4)+3(3k-4)=0⇒4k2-13k+10=0⇒k=2,5/4∴ Sum of values of K=2+54=134=3.25

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If the system of equations $x + k y + 3 z = 0,$ $k x + 2 y + 2 z = 0,$ $2 x + 3 y + 4 z = 0$ admits of non-trivial solution, then sum of values of $' k'$