Answer
$[A|B]=\left[\begin{array}{rrr|r}
{1}&{-1}&{-1}&{10}\\
{2}&{1}&{2}&{-1}\\
{-3}&{4}&{0}&{5}\\
{4}&{-5}&{1}&{0}\end{array}\right]$
Work Step by Step
Standard form of a linear equation:
$a_{i1}x_{1}+a_{i2}x_{2}+\cdots+a_{in}x_{n}=b_{i}$
... the index i indicates that it is the i-th equation of a system of equations.
Augmented matrix $[A|B]$ of a system written in standard form:
- has as many rows as there are equations,
- has one more column than there are variables,
- has the constants of the RHS in the last column, $B=[b_{i}]$
- has the entries of the coefficient matrix $A=[a_{ij}]$ to the left of the last column.
---
The system is in standard form.
$ A=\left[\begin{array}{rrr}
1 & -1 & -1\\
2 & 1 & 2\\
-3 & 4 & 0\\
4 & -5 & 1
\end{array}\right],\quad B=\left[\begin{array}{l}
10\\
-1\\
5\\
0
\end{array}\right]$
$[A|B]=\left[\begin{array}{rrr|r}
{1}&{-1}&{-1}&{10}\\
{2}&{1}&{2}&{-1}\\
{-3}&{4}&{0}&{5}\\
{4}&{-5}&{1}&{0}\end{array}\right]$
