Linear Algebra and Its Applications · Problem 2.4.3

Vector Spaces — Gilbert Strang

Mathematics · four-fundamental-subspaces

Problem

Find the dimension and a basis for the four fundamental subspaces for

A = \begin{bmatrix} 1 & 2 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 2 & 0 & 1 \end{bmatrix} \quad \text{and} \quad U = \begin{bmatrix} 1 & 2 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{bmatrix}.