A First Course in Linear Algebra · Problem LI.C60

Vectors — Robert Beezer

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

Problem

For the matrix

A

below, find a set of vectors

S

so that (1)

S

is linearly independent, and (2) the span of

S

equals the null space of

A

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

. (See Exercise SS.C60.)

A = \begin{bmatrix} 1 & 1 & 6 & -8 \\ 1 & -2 & 0 & 1 \\ -2 & 1 & -6 & 7 \end{bmatrix}