A First Course in Linear Algebra · Problem LI.C32

Vectors — Robert Beezer

Mathematics — Linear Algebra · linear-independence-null-spaces

Problem

Find a set of column vectors,

T

, such that (1) the span of

T

is the null space of

B

\langle T \rangle = \mathcal{N}(B)

and (2)

T

is a linearly independent set.

B = \begin{bmatrix} 2 & 1 & 1 & 1 \\ -4 & -3 & 1 & -7 \\ 1 & 1 & -1 & 3 \end{bmatrix}