If the following three linear equations have a non-trivial solution, then $$ \begin{aligned} &x+4 a y+a z=0 \\ &x+3 b y+b z=0 \\ &x+2 c y+c z=0 \end{aligned} $$

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If the following three linear equations have a non-trivial solution, then $$ \begin{aligned} &x+4 a y+a z=0 \\ &x+3 b y+b z=0 \\ &x+2 c y+c z=0 \end{aligned} $$

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kritika · Answer 1 · 2021-12-27T07:13:40+0000

Ans: (C)
Hint : To have non-trivial solution, $\left|\begin{array}{lll}1 & 4 a & a \\ 1 & 3 b & b \\ 1 & 2 c & c\end{array}\right|=0 \Rightarrow \frac{1}{c}+\frac{1}{a}=\frac{2}{b}$

If the following three linear equations have a non-trivial solution, then $$ \begin{aligned} &x+4 a y+a z=0 \\ &x+3 b y+b z=0 \\ &x+2 c y+c z=0 \end{aligned} $$

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