Exercise 4

Consider the following matrices: $$A = \left[\begin{array}{rrrr} 3 & 0 & -1 & 1 \\ 1 & -1 & 3 & 7 \\ 3 & -2 & 1 & 5 \\ -1 & 2 & 2 & 3 \\ \end{array}\right],~~~ B = \left[\begin{array}{rrrr} 3 & 0 & -1 & 4 \\ 1 & -1 & 3 & -1 \\ 3 & -2 & 1 & 3 \\ -1 & 2 & 2 & 1 \\ \end{array}\right]$$. Do the columns of $A$ span $\real^4$? Do the columns of $B$ span $\real^4$?