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The system of equations $x-2 y+3 z=5$, $2 x-2 y+z=0,-x+2 y-3 z=6$ has
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Verified Answer
The correct answer is:
no solution
Given system of equations,
$$
\begin{aligned}
\because \Delta & =\left|\begin{array}{ccc}
1 & -2 & 3 \\
2 & -2 & 1 \\
-1 & 2 & -3
\end{array}\right|=1(6-2)+2(-6+1)+3(4-2) \\
& =4-10+6=0 \\
\Delta_1 & =\left|\begin{array}{ccc}
5 & -2 & 3 \\
0 & -2 & 1 \\
6 & 2 & -3
\end{array}\right|=5(6-2)+2(0-6)+3(0+12) \\
& =20-12+36 \neq 0
\end{aligned}
$$
So, no solution.
$$
\begin{aligned}
\because \Delta & =\left|\begin{array}{ccc}
1 & -2 & 3 \\
2 & -2 & 1 \\
-1 & 2 & -3
\end{array}\right|=1(6-2)+2(-6+1)+3(4-2) \\
& =4-10+6=0 \\
\Delta_1 & =\left|\begin{array}{ccc}
5 & -2 & 3 \\
0 & -2 & 1 \\
6 & 2 & -3
\end{array}\right|=5(6-2)+2(0-6)+3(0+12) \\
& =20-12+36 \neq 0
\end{aligned}
$$
So, no solution.
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