Exercise CRS.C35 Robert Beezer

For the matrix $A$ below, find two different linearly independent sets whose spans equal the column space of $A$, $\csp{A}$, such that

  1. the elements are each columns of $A$.
  2. the set is obtained by a procedure that is substantially different from the procedure you use in part (1).
\begin{align*} A&= \begin{bmatrix} 3 & 5 & 1 & -2 \\ 1 & 2 & 3 & 3 \\ -3 & -4 & 7 & 13 \end{bmatrix} \end{align*}

Solution