Answer
$[A|B]=\left[\begin{array}{rrrr|r}
{1}&{-1}&{2}&{-1}&{5}\\
{1}&{3}&{-4}&{2}&{2}\\
{3}&{-1}&{-5}&{-1}&{-1}\end{array}\right]$
Work Step by Step
The standard form of a linear equation can be expressed as:
$a_{i1}x_{1}+a_{i2}x_{2}+...+a_{in}x_{n}=b_{i}$
where, the index $i$ indicates that it is the $i$-th equation of a system of equations.
In order to write the augmented matrix $[A|B]$ of a system of equations in standard form, we must follow some important points:
1. To express a system in matrix form, we must extract the coefficients of the variables and constants.
2. Draw a vertical line to separate the coefficient entries from the constants (essentially replacing the equal signs).
3. The entries of the coefficient matrix $A=[a_{ij}]$ must be placed to the left of the lline.
4. The constants of the $B=[b_{i}]$ must be placed to the right of the line.
Now, we have:
$ A=\left[\begin{array}{rrrrr}
1 & -1 & 2 & -1 & \\
1 & 3 & -4 & 2 & \\
3 & -1 & -5 & -1 &
\end{array}\right]$ and $ B=\left[\begin{array}{l}
5\\
2\\
-1
\end{array}\right]$
Finally, we can write the system as an augmented matrix $[A|B]$ as follows:
$[A|B]=\left[\begin{array}{rrrr|r}
{1}&{-1}&{2}&{-1}&{5}\\
{1}&{3}&{-4}&{2}&{2}\\
{3}&{-1}&{-5}&{-1}&{-1}\end{array}\right]$
