If the system of equations mathrm{x}+4 mathrm | vedclass

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Question

$\Delta=\left|\begin{array}{ccc}1 & 4 & -1 \ 7 & 9 & \mu \ 5 & 1 & 2\end{array}ight|=0$

$\Rightarrow(18-\mu)-4(14-5 \mu

Vedclass · Accepted Answer

$-3$

Vedclass · Answer

$\Delta=\left|\begin{array}{ccc}1 & 4 & -1 \ 7 & 9 & \mu \ 5 & 1 & 2\end{array}ight|=0$

$\Rightarrow(18-\mu)-4(14-5 \mu)-(7-45)=0 \Rightarrow \mu=0$

$\Delta=\Delta_{\mathrm{x}}=\Delta_{\mathrm{y}}=\Delta_{\mathrm{z}}=0$ (For infinite solution)

$\Delta_x=\left|\begin{array}{ccc}\lambda & 4 & -1 \ -3 & 9 & \mu \ -1 & 1 & 2\end{array}ight|=0$

$ \lambda(18-\mu)-4(-6+\mu)-1(-3+9)=0 $

$ 18 \lambda+24-6=0 \Rightarrow \lambda=-1$

If the system of equations $\mathrm{x}+4 \mathrm{y}-\mathrm{z}=\lambda$, $7 x+9 y+\mu z=-3,5 x+y+2 z=-1$ has infinitely many solutions, then $(2 \mu .+3 \lambda)$ is equal to :

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