The system of equations $$ \begin{aligned} &\lambda x+y+3 z=0 \\ &2 x+\mu y-z=0 \\ &5 x+7 y+z=0 \end{aligned} $$ has infinitely many solutions in $\mathbb{R}$. Then,

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The system of equations $$ \begin{aligned} &\lambda x+y+3 z=0 \\ &2 x+\mu y-z=0 \\ &5 x+7 y+z=0 \end{aligned} $$ has infinitely many solutions in $\mathbb{R}$. Then,

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kritika · Answer 1 · 2021-12-27T04:37:18+0000

Ans: (C)

Hint: $\left|\begin{array}{ccc}\lambda & 1 & 3 \\ 2 & \mu & -1 \\ 5 & 7 & 1\end{array}\right|=0$ $\lambda(\mu+7)-1(2+5)+3(14-5 \mu)=0$ or, $\lambda \mu+7 \lambda-7+42-15 \mu=0$ or, $\lambda \mu+7 \lambda-15 \mu=-35$ if $\lambda=1, \mu=3$, satisfies.

The system of equations $$ \begin{aligned} &\lambda x+y+3 z=0 \\ &2 x+\mu y-z=0 \\ &5 x+7 y+z=0 \end{aligned} $$ has infinitely many solutions in \(\mathbb{R}\). Then,

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