Name:      

Directions: Show all work. No credit for answers without work.

1. [6 points] Find the general solution of the system with the following augmented matrix.

   $$\left[\begin{array}{cccccc}\hfill 3& \hfill 0& \hfill -3& \hfill 6& \hfill -2& \hfill -3\\ \hfill 3& \hfill 0& \hfill -3& \hfill 6& \hfill -3& \hfill -6\\ \hfill 10& \hfill 1& \hfill -6& \hfill 21& \hfill -3& \hfill 3\\ \hfill -8& \hfill 0& \hfill 8& \hfill -16& \hfill 3& \hfill 1\end{array}\right]$$

2. [2 parts, 1.5 points each] Let $A$ be a $(8\times 4)$-matrix such that each of the four columns is a pivot column.

   1. Give the reduced row-echelon form of $A$.
   2. Describe the row-echelon form(s) of $A$.
3. [1 point] Let $A$ be an $(m\times n)$ augmented matrix that represents a linear system with a unique solution. What can be said about the relationship between $m$ and $n$?