Answer
$ \begin{bmatrix}
1&1 &1 &2\\
0& 1 & 0 & -1 \\
0&0&2&4
\end{bmatrix}$.
Work Step by Step
The augmented matrix is
$\begin{bmatrix}
1&1 &1 &2\\
2 & 3 & 2 & 3 \\
0&-2&2&6
\end{bmatrix}$
Perform the given operations.
$R_2\rightarrow R_2-2R_1$
$\Rightarrow \begin{bmatrix}
1&1 &1 &2\\
2 -2(1)& 3 -2(1) & 2 -2(1) & 3 -2(2) \\
0&-2&2&6
\end{bmatrix}$
Simplify.
$\Rightarrow \begin{bmatrix}
1&1 &1 &2\\
2 -2& 3 -2 & 2 -2 & 3 -4 \\
0&-2&2&6
\end{bmatrix}$
$\Rightarrow \begin{bmatrix}
1&1 &1 &2\\
0& 1 & 0 & -1 \\
0&-2&2&6
\end{bmatrix}$
Perform the given operations.
$R_3\rightarrow R_3+2R_2$
$\Rightarrow \begin{bmatrix}
1&1 &1 &2\\
0& 1 & 0 & -1 \\
0+2(0)&-2+2(1)&2+2(0)&6+2(-1)
\end{bmatrix}$
Simplify.
$\Rightarrow \begin{bmatrix}
1&1 &1 &2\\
0& 1 & 0 & -1 \\
0+0&-2+2&2+0&6-2
\end{bmatrix}$
$\Rightarrow \begin{bmatrix}
1&1 &1 &2\\
0& 1 & 0 & -1 \\
0&0&2&4
\end{bmatrix}$
The above matrix is the upper triangular form.
