A First Course in Linear Algebra · Problem CRS.C35

Matrices — Robert Beezer

Mathematics — Linear Algebra · column-space-basis

Problem

For the matrix

A

below, find two different linearly independent sets whose spans equal the column space of

A

\mathcal{C}(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).

A = \begin{bmatrix} 3 & 5 & 1 & -2 \\ 1 & 2 & 3 & 3 \\ -3 & -4 & 7 & 13 \end{bmatrix}