Exhibit matrices with specific properties

mark

For each of the following scenarios, write down a $2\times3$ augmented matrix in reduced row echelon form that represents that scenario

1. A system with exactly one solution
2. A system with infinitely many solutions
3. A system with no solutions

Student23

An augmented matrix in reduced row echelon form that represents:
1- a system with exactly one solution
$$
\left(\begin{matrix}1 & 0 & 3 \\ 0 & 1 & 2 \end{matrix}\right)
$$

2- a system with infinitely many solutions
$$
\left(\begin{matrix}1 & 2 & 4 \\ 0 & 0 & 0 \end{matrix}\right)
$$

3- a system with no solutions
$$
\left(\begin{matrix}1 & 0 & 7 \\ 0 & 0 & 1 \end{matrix}\right)
$$