Answer
\[
\left[
\begin{array}{ccc|c}
2 & 1 & 1 &3 \\
3 & -4 & 2 &-7\\1&1&1&2
\end{array}
\right]
\]
Work Step by Step
We will write the given equations in such a form that the variables terms are on the left-hand side and the constants on the right-hand side.
Thus, we have:
$2x+y+z=3 \quad\quad \text{(Add 3 to both sides of the first equation.)}\\ 3x-4y+2z=-7 \quad\quad \text{(Subtract 7 from both sides of the first equation.)}\\x+y+z=2 \quad\quad \text{(Add 2 to both sides of the third equation.)}$
We transform the above equations into a $3 \times 4$ matrix such that the coefficients of the variables are on the left-hand side and the constants on the right-hand side of the vertical bar.
Therefore, we write the $3 \times 4$ matrix can be expressed as:
\[
\left[
\begin{array}{ccc|c}
2 & 1 & 1 &3 \\
3 & -4 & 2 &-7\\1&1&1&2
\end{array}
\right]
\]
