A First Course in Linear Algebra · Problem CRS.C31

Matrices — Robert Beezer

Mathematics — Linear Algebra · column-space-basis

Problem

For the matrix

A

below find a set of vectors

T

meeting the following requirements: (1) the span of

T

is the column space of

A

, that is,

\langle T \rangle = \mathcal{C}(A)

, (2)

T

is linearly independent, and (3) the elements of

T

are columns of

A

A = \begin{bmatrix} 2 & 1 & 4 & -1 & 2 \\ 1 & -1 & 5 & 1 & 1 \\ -1 & 2 & -7 & 0 & 1 \\ 2 & -1 & 8 & -1 & 2 \end{bmatrix}