Answer
$[A|B]=\left[\begin{array}{rrr|r}
{2}&{3}&{-4}&{0}\\
{1}&{0}&{-5}&{-2}\\
{1}&{2}&{-3}&{-2}\end{array}\right]$
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.
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Rewrite the system in standard form (eq.2!)
$\left\{\begin{array}{llll}
2x & +3y & -4z & =0\\
x & & -5z & =-2\\
x & +2y & -3z & =-2
\end{array}\right.$
$ A=\left[\begin{array}{lll}
2 & 3 & -4\\
1 & 0 & -5\\
1 & 2 & -3
\end{array}\right],\quad B=\left[\begin{array}{l}
0\\
-2\\
-2
\end{array}\right]$
$[A|B]=\left[\begin{array}{rrr|r}
{2}&{3}&{-4}&{0}\\
{1}&{0}&{-5}&{-2}\\
{1}&{2}&{-3}&{-2}\end{array}\right]$
