The following system of linear equations&nbsp | vedclass

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Question

$7 \mathrm{x}+6 \mathrm{y}-2 \mathrm{z}=0\dots(1)$

$3 x+4 y+2 z=0\dots(2)$

$\mathrm{x}-2 \mathrm{y}-6 \mathrm{z}=0\dots(3)$

$\Delta=\left|\be

Vedclass · Accepted Answer

infinitely many solutions, $(\mathrm{x}, \mathrm{y}, \mathrm{z})$ satisfying $x=2 z$

Vedclass · Answer

$7 \mathrm{x}+6 \mathrm{y}-2 \mathrm{z}=0\dots(1)$

$3 x+4 y+2 z=0\dots(2)$

$\mathrm{x}-2 \mathrm{y}-6 \mathrm{z}=0\dots(3)$

$\Delta=\left|\begin{array}{ccc}{7} & {6} & {-2} \ {3} & {4} & {2} \ {1} & {-2} & {-6}\end{array}ight|=0 \Rightarrow$ infinite solutions

Now $(1)+(2) \Rightarrow y=-x$ put in $(1),(2)$ and $(3)$

all will lead to $x=2 z$

The following system of linear equations $7 x+6 y-2 z=0$ ; $3 x+4 y+2 z=0$ ; ${x}-2{y}-6{z}=0,$ has

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