Answer
$[A|B]=\left[\begin{array}{rr|r}
{ 4/3 }&{-3/2 } &{ 3/4 }\\
{ -1/4 }&{ 1/3 } &{ 2/3 }\end{array}\right]$
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}{ll}
4/3 & -3/2\\
-1/4 & 1/3
\end{array}\right],\quad B=\left[\begin{array}{l}
3/4\\
2/3
\end{array}\right]$
$[A|B]=\left[\begin{array}{rr|r}
{ 4/3 }&{-3/2 } &{ 3/4 }\\
{ -1/4 }&{ 1/3 } &{ 2/3 }\end{array}\right]$