1. Write the column space of the matrix below as the span of a set of three vectors and explain your choice of method. \begin{equation*} \begin{bmatrix} 1 & 3 & 1 & 3\\ 2 & 0 & 1 & 1\\ -1 & 2 & 1 & 0 \end{bmatrix} \end{equation*}
2. Suppose that $A$ is an $n\times n$ nonsingular matrix. What can you say about its column space?
3. Is the vector $\colvector{0\\5\\2\\3}$ in the row space of the following matrix? Why or why not? \begin{equation*} \begin{bmatrix} 1 & 3 & 1 & 3\\ 2 & 0 & 1 & 1\\ -1 & 2 & 1 & 0 \end{bmatrix} \end{equation*}