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The system of linear equations : $x+y+z=0,2 x$ $+y-z=0,3 x+2 y=0$ has :
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Verified Answer
The correct answer is:
an infinitely many solution
The system is homogenuous system. $\therefore$ it has either unique solution or infinite many solution depend on $|\mathrm{A}|$
$$
\begin{aligned}
\therefore|A| &=\left|\begin{array}{rrr}
1 & 1 & 1 \\
2 & 1 & -1 \\
3 & 2 & 0
\end{array}\right|=2 \times 1+1(-3)+(4-3) \\
&=2-3+1=0
\end{aligned}
$$
$$
\begin{aligned}
\therefore|A| &=\left|\begin{array}{rrr}
1 & 1 & 1 \\
2 & 1 & -1 \\
3 & 2 & 0
\end{array}\right|=2 \times 1+1(-3)+(4-3) \\
&=2-3+1=0
\end{aligned}
$$
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