Answer
$\begin{bmatrix}
1&2 &1 &-7\\
0 & 1 & 0 & -3 \\
0&0&2&2
\end{bmatrix}$
Work Step by Step
The augmented matrix is
$\begin{bmatrix}
1&2 &1 &-7\\
1 & 3 & 1 & -10 \\
-2&-3&0&13
\end{bmatrix}$
Perform the given operations.
$R_2\rightarrow R_2-R_1$
$\Rightarrow \begin{bmatrix}
1&2 &1 &-7\\
1-1 & 3-2 & 1-1 & -10-(-7) \\
-2&-3&0&13
\end{bmatrix}$
Simplify.
$\Rightarrow \begin{bmatrix}
1&2 &1 &-7\\
1-1 & 3-2 & 1-1 & -10+7 \\
-2&-3&0&13
\end{bmatrix}$
$\Rightarrow \begin{bmatrix}
1&2 &1 &-7\\
0 & 1 & 0 & -3 \\
-2&-3&0&13
\end{bmatrix}$
Perform the given operations.
$R_3\rightarrow R_3+2R_1$
$\Rightarrow \begin{bmatrix}
1&2 &1 &-7\\
0 & 1 & 0 & -3 \\
-2+2(1)&-3+2(2)&0+2(1)&13+2(-7)
\end{bmatrix}$
Simplify.
$\Rightarrow \begin{bmatrix}
1&2 &1 &-7\\
0 & 1 & 0 & -3 \\
-2+2&-3+4&0+2&13-14
\end{bmatrix}$
$\Rightarrow \begin{bmatrix}
1&2 &1 &-7\\
0 & 1 & 0 & -3 \\
0&1&2&-1
\end{bmatrix}$
Perform the given operations.
$R_3\rightarrow R_3-R_2$
$\Rightarrow \begin{bmatrix}
1&2 &1 &-7\\
0 & 1 & 0 & -3 \\
0-0&1-1&2-0&-1-(-3)
\end{bmatrix}$
Simplify.
$\Rightarrow \begin{bmatrix}
1&2 &1 &-7\\
0 & 1 & 0 & -3 \\
0-0&1-1&2-0&-1+3
\end{bmatrix}$
$\Rightarrow \begin{bmatrix}
1&2 &1 &-7\\
0 & 1 & 0 & -3 \\
0&0&2&2
\end{bmatrix}$
The above matrix is the upper triangular form.
