Answer
$[A|B]=\left[\begin{array}{rr|r}
{2}&{3}&{6}\\
{4}&{-6}&{-2}\end{array}\right]$
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.
---
Rewrite the system in standard form,
$\left\{\begin{array}{l}
2x+3y=6\\
4x-6y=-2
\end{array}\right.$
$ A=\left[\begin{array}{ll}
2 & 3\\
4 & -6
\end{array}\right],\quad B=\left[\begin{array}{l}
6\\
-2
\end{array}\right]$
$[A|B]=\left[\begin{array}{rr|r}
{2}&{3}&{6}\\
{4}&{-6}&{-2}\end{array}\right]$
