A First Course in Linear Algebra · Problem SS.C60

Vectors — Robert Beezer

Mathematics — Linear Algebra · spanning-sets-null-spaces

Problem

For the matrix

A

below, find a set of vectors

S

so that the span of

S

equals the null space of

A

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

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