Exercise4

Consider the following matrices:

\begin{equation*} A = \left[\begin{array}{rrrr} 3 \amp 0 \amp -1 \amp 1 \\ 1 \amp -1 \amp 3 \amp 7 \\ 3 \amp -2 \amp 1 \amp 5 \\ -1 \amp 2 \amp 2 \amp 3 \\ \end{array}\right], B = \left[\begin{array}{rrrr} 3 \amp 0 \amp -1 \amp 4 \\ 1 \amp -1 \amp 3 \amp -1 \\ 3 \amp -2 \amp 1 \amp 3 \\ -1 \amp 2 \amp 2 \amp 1 \\ \end{array}\right] \text{.} \end{equation*}

Do the columns of \(A\) span \(\real^4\text{?}\) Do the columns of \(B\) span \(\real^4\text{?}\)

in-context