A First Course in Linear Algebra · Problem C15

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · subspace-membership

Problem

Working within the vector space

\mathbb{C}^3

, determine if

\mathbf{b} = \begin{bmatrix} 4 \\ 3 \\ 1 \end{bmatrix}

is in the subspace

W

W = \left\langle \left\{ \begin{bmatrix} 3 \\ 2 \\ 3 \end{bmatrix}, \begin{bmatrix} 1 \\ 0 \\ 3 \end{bmatrix}, \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix}, \begin{bmatrix} 2 \\ 1 \\ 3 \end{bmatrix} \right\} \right\rangle