##### Itemd

Suppose that the augmented matrix of a system of linear equations has the following shape where $$*$$ could be any real number.

\begin{equation*} \left[ \begin{array}{rrrrr|r} * \amp * \amp * \amp * \amp * \amp * \\ * \amp * \amp * \amp * \amp * \amp * \\ * \amp * \amp * \amp * \amp * \amp * \\ \end{array} \right]. \end{equation*}
1. How many equations are there in this system and how many unknowns?

2. Based on our earlier discussion in Section 1, do you think it's possible that this system has exactly one solution, infinitely many solutions, or no solutions?

3. Suppose that this augmented matrix is row equivalent to

\begin{equation*} \left[ \begin{array}{rrrrr|r} 1 \amp 2 \amp 0 \amp 0 \amp 3 \amp 2 \\ 0 \amp 0 \amp 1 \amp 2 \amp -1 \amp -1 \\ 0 \amp 0 \amp 0 \amp 0 \amp 0 \amp 0 \\ \end{array} \right]. \end{equation*}

Make a choice for the names of the unknowns and write the corresponding system of linear equations. Does the system have exactly one solution, infinitely many solutions, or no solutions?

in-context