A First Course in Linear Algebra · Problem LI.C31

Vectors — Robert Beezer

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

Problem

For the matrix

A

below, find a linearly independent set

S

so that the null space of

A

is spanned by

S

, that is,

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

A = \begin{bmatrix} -1 & -2 & 2 & 1 & 5 \\ 1 & 2 & 1 & 1 & 5 \\ 3 & 6 & 1 & 2 & 7 \\ 2 & 4 & 0 & 1 & 2 \end{bmatrix}