Value of k ∈ R , for which following system of linear equations 3 x-y+4 z=3 x+2 y-3 x=-2 6 x+5 y+k

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3 and 4 .Determinants and Matrices

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The value of $k \in R$, for which the following system of linear equations

$3 x-y+4 z=3$

$x+2 y-3 x=-2$

$6 x+5 y+k z=-3$

has infinitely many solutions, is:

A

$3$

B

$-3$

C

$5$

D

$-5$

(JEE MAIN-2021)

Solution

$\left|\begin{array}{ccc}3 & -1 & 4 \\ 1 & 2 & -3 \\ 6 & 5 & K\end{array}\right|=0$

$\Rightarrow 3(2 \mathrm{~K}+15)+\mathrm{K}+18-28=0$

$\Rightarrow 7 \mathrm{~K}+35=0 \Rightarrow \mathrm{K}-5$

Standard 12

Mathematics

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