Answer
$\begin{bmatrix}
-12&0 &-8&-36\\
0 & -6 & 4 & 24 \\
0&0&1&3
\end{bmatrix}$.
Work Step by Step
The augmented matrix is
$\begin{bmatrix}
3&0 &2&9\\
4 & 1 & 2 & 8 \\
3&2&1&2
\end{bmatrix}$
Perform the given operations.
$R_1\rightarrow -4R_1,R_2\rightarrow 3R_2$ and $R_3\rightarrow 4R_3$
$\Rightarrow \begin{bmatrix}
-4(3)&-4(0) &-4(2)&-4(9)\\
3(4) & 3(1) & 3(2) & 3(8) \\
4(3)&4(2)&4(1)&4(2)
\end{bmatrix}$
Simplify.
$\Rightarrow \begin{bmatrix}
-12&0 &-8&-36\\
12 & 3 & 6 & 24 \\
12&8&4&8
\end{bmatrix}$
Perform the given operations.
$R_2\rightarrow R_2+R_1$ and $R_3\rightarrow R_3+R_1$
$\Rightarrow \begin{bmatrix}
-12&0 &-8&-36\\
12-12 & 3+0 & 6-8 & 24-36 \\
12-12&8+0&4-8&8-36
\end{bmatrix}$
Simplify.
$\Rightarrow \begin{bmatrix}
-12&0 &-8&-36\\
0 & 3 & -2 & -12 \\
0&8&-4&-28
\end{bmatrix}$
Perform the given operations.
$R_3\rightarrow R_3/4$
$\Rightarrow \begin{bmatrix}
-12&0 &-8&-36\\
0 & 3 & -2 & -12 \\
0/4&8/4&-4/4&-28/4
\end{bmatrix}$
Simplify.
$\Rightarrow \begin{bmatrix}
-12&0 &-8&-36\\
0 & 3 & -2 & -12 \\
0&2&-1&-7
\end{bmatrix}$
Perform the given operations.
$R_2\rightarrow -2R_2$ and $R_3\rightarrow 3R_3$
$\Rightarrow \begin{bmatrix}
-12&0 &-8&-36\\
-2(0) & -2(3) &- 2(-2) &- 2(-12) \\
3(0)&3(2)&3(-1)&3(-7)
\end{bmatrix}$
Simplify.
$\Rightarrow \begin{bmatrix}
-12&0 &-8&-36\\
0 & -6 & 4 & 24 \\
0&6&-3&-21
\end{bmatrix}$
Perform the given operations.
$R_3\rightarrow R_3+R_2$
$\Rightarrow \begin{bmatrix}
-12&0 &-8&-36\\
0 & -6 & 4 & 24 \\
0+0&6-6&-3+4&-21+24
\end{bmatrix}$
Simplify.
$\Rightarrow \begin{bmatrix}
-12&0 &-8&-36\\
0 & -6 & 4 & 24 \\
0&0&1&3
\end{bmatrix}$
The above matrix is the upper triangular form.
