[
2
4
6
∣
18
4
5
6
∣
24
3
1
−
2
∣
4
]
\begin{bmatrix}2 & 4 & 6 & | & 18\\4 & 5 & 6 & | & 24\\3 & 1 & -2 & | & 4\end{bmatrix}
⎣
⎢
⎡
2
4
3
4
5
1
6
6
−
2
∣
∣
∣
1
8
2
4
4
⎦
⎥
⎤
R
3
→
R
3
−
3
R
1
→
{
3
x
1
+
1
x
2
−
2
x
3
=
4
−
3
(
1
)
x
1
+
3
(
2
)
x
2
+
3
(
3
)
x
3
=
3
(
9
)
‾
−
5
x
2
−
11
x
3
=
−
23
\underrightarrow{\begin{subarray}{l}R_3\to R_3-3R_1\end{subarray}}\begin{cases}\kern{1.2em}{\color{black}3} x_1 +{\color{black}1} x_2 -{\color{black}2} x_3={\color{black}4}\\\underline{- \kern{.5em}3({\color{black}1})x_1 +3({\color{black}2})x_2 +3({\color{black}3})x_3=3({\color{black}9})} \\\kern{4.2em}{\color{#6F8DD8}-5} x_2 -{\color{#6F8DD8}11} x_3={\color{#6F8DD8}-23}\end{cases}
R
3
→
R
3
−
3
R
1
⎩
⎪
⎪
⎨
⎪
⎪
⎧
3
x
1
+
1
x
2
−
2
x
3
=
4
−
3
(
1
)
x
1
+
3
(
2
)
x
2
+
3
(
3
)
x
3
=
3
(
9
)
−
5
x
2
−
1
1
x
3
=
−
2
3