Linear Algebra and Its Applications · Problem 2.4.17

Vector Spaces — Gilbert Strang

Mathematics · four-fundamental-subspaces

Problem

Find a matrix

A

that has

\mathbf{V}

as its row space, and a matrix

B

that has

\mathbf{V}

as its nullspace, if

\mathbf{V}

is the subspace spanned by

\begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix}, \quad \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix}, \quad \begin{bmatrix} 1 \\ 5 \\ 0 \end{bmatrix}.