If the system of linear equations 2 x + | vedclass

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Question

$\quad\left|\begin{array}{ccc}2 & 1 & -1 \ 1 & -3 & 2 \ 1 & 4 & \delta\end{array}ight|=0$

$\Rightarrow \delta=-3$

An

Vedclass · Accepted Answer

$3$

Vedclass · Answer

$\quad\left|\begin{array}{ccc}2 & 1 & -1 \ 1 & -3 & 2 \ 1 & 4 & \delta\end{array}ight|=0$

$\Rightarrow \delta=-3$

And $\left|\begin{array}{ccr}7 & 1 & -1 \ 1 & -3 & 2 \ K & 4 & -3\end{array}ight|=0 \Rightarrow K =6$

$\Rightarrow \delta+ K =3$

Alternate

$2 x + y - z =7$             $\dots(1)$

$x-3 y+2 z=1$             $\dots(2)$

$x +4 y +\delta z = k$            $\dots(3)$

Equation $(2) + (3)$

We get $2 x+y+(2+\delta) z=1+K$           $\dots(4)$

For infinitely solution

Form equation $(1)$ and $(4)$

$2+\delta=-1 \Rightarrow \delta=-3$

$1+ k =7 \Rightarrow k =6$

$\delta+ k =3$

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

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