Linear Algebra and Its Applications · Problem 2.4.22

Vector Spaces — Gilbert Strang

Mathematics · four-fundamental-subspaces

Problem

Without elimination, find dimensions and bases for the four subspaces for

A = \begin{bmatrix} 0 & 3 & 3 & 3 \\ 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} 1 & 1 \\ 4 & 4 \\ 5 & 5 \end{bmatrix}.