Answer
$\begin{bmatrix}
15&6 &3&3\\
0 & 6 & -2 & -23\\
0&0&-2&-47
\end{bmatrix}$
Work Step by Step
The augmented matrix is
$\begin{bmatrix}
5&2 &1&1\\
3 & 0 & 1 & -4 \\
5&1&1&-3
\end{bmatrix}$
Perform the given operations.
$R_1\rightarrow 3R_1,R_2\rightarrow -5R_2$ and $R_3\rightarrow -3R_3$
$\begin{bmatrix}
3( 5)&3(2) &3(1)&3(1)\\
-5(3) & -5(0) & -5(1) & -5(-4) \\
-3(5)&-3(1)&-3(1)&-3(-3)
\end{bmatrix}$
Simplify.
$\begin{bmatrix}
15&6 &3&3\\
-15 & 0 & -5 & 20 \\
-15&-3&-3&9
\end{bmatrix}$
Perform the given operations.
$R_2\rightarrow R_2+R_1$ and $R_3\rightarrow R_3+R_1$
$\begin{bmatrix}
15&6 &3&3\\
-15+15 & 0+6 & -5+3 & 20 +3\\
-15+15&-3+6&-3+3&9+3
\end{bmatrix}$
Simplify.
$\begin{bmatrix}
15&6 &3&3\\
0 & 6 & -2 & -23\\
0&3&0&12
\end{bmatrix}$
Perform the given operations.
$R_3\rightarrow -2R_3$
$\begin{bmatrix}
15&6 &3&3\\
0 & 6 & -2 & -23\\
-2(0)&-2(3)&-2(0)&-2(12)
\end{bmatrix}$
Simplify.
$\begin{bmatrix}
15&6 &3&3\\
0 & 6 & -2 & -23\\
0&-6&0&-24
\end{bmatrix}$
Perform the given operations.
$R_3\rightarrow R_3+R_2$
$\begin{bmatrix}
15&6 &3&3\\
0 & 6 & -2 & -23\\
0+0&-6+6&0-2&-24-23
\end{bmatrix}$
Simplify.
$\begin{bmatrix}
15&6 &3&3\\
0 & 6 & -2 & -23\\
0&0&-2&-47
\end{bmatrix}$
The above matrix is the upper triangular form.
