Exercise LI.C33 Robert Beezer

Find a set $S$ so that $S$ is linearly independent and $\nsp{A}=\spn{S}$, where $\nsp{A}$ is the null space of the matrix $A$ below. \begin{align*} A&= \begin{bmatrix} 2 & 3 & 3 & 1 & 4 \\ 1 & 1 & -1 & -1 & -3 \\ 3 & 2 & -8 & -1 & 1 \end{bmatrix} \end{align*}

Solution