Linear Algebra and Its Applications · Problem 2.4.2

Vector Spaces — Gilbert Strang

Mathematics · four-fundamental-subspaces

Problem

Find the dimension and construct a basis for the four subspaces associated with each of the matrices

A = \begin{bmatrix} 0 & 1 & 4 & 0 \\ 0 & 2 & 8 & 0 \end{bmatrix} \quad \text{and} \quad U = \begin{bmatrix} 0 & 1 & 4 & 0 \\ 0 & 0 & 0 & 0 \end{bmatrix}.