Consider the system of linear equations: $ \begin{aligned} & x_1+2 x_2+x_3=3 \\ & 2 x_1+3 x_2+x_3=3 \\ & 3…
Consider the system of linear equations:
$
\begin{aligned}
& x_1+2 x_2+x_3=3 \\
& 2 x_1+3 x_2+x_3=3 \\
& 3 x_1+5 x_2+2 x_3=1
\end{aligned}
$
The system has
exactly 3 solutions
a unique solution
no solution
infinite number of solutions
Solution
$
\begin{aligned}
& D=\left|\begin{array}{lll}
1 & 2 & 1 \\
2 & 3 & 1 \\
3 & 5 & 2
\end{array}\right|=0 \\
& D_1=\left|\begin{array}{lll}
3 & 2 & 1 \\
3 & 3 & 1 \\
1 & 5 & 2
\end{array}\right| \neq 0
\end{aligned}
$
$\Rightarrow$ Given system, does not have any solution.
$\Rightarrow$ No solution.