Linear Algebra and Its Applications · Problem 2.4.29

Vector Spaces — Gilbert Strang

Mathematics · four-fundamental-subspaces

Problem

Without computing

A

, find bases for the four fundamental subspaces:

A = \begin{bmatrix} 1 & 0 & 0 \\ 6 & 1 & 0 \\ 9 & 8 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 1 & 2 & 3 \\ 0 & 0 & 1 & 2 \end{bmatrix}.