A First Course in Linear Algebra · Problem LI.C33

Vectors — Robert Beezer

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

Problem

Find a set

S

so that

S

is linearly independent and

\mathcal{N}(A) = \langle S \rangle

, where

\mathcal{N}(A)

is the null space of the matrix

A

below.

A = \begin{bmatrix} 2 & 3 & 3 & 1 & 4 \\ 1 & 1 & -1 & -1 & -3 \\ 3 & 2 & -8 & -1 & 1 \end{bmatrix}