A First Course in Linear Algebra · Problem SS.RQ.1

Vectors — Robert Beezer

Mathematics — Linear Algebra · spanning-sets

Problem

Let

S

be the set of three vectors below.

S = \left\{ \begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix}, \begin{bmatrix} 3 \\ -4 \\ 2 \end{bmatrix}, \begin{bmatrix} 4 \\ -2 \\ 1 \end{bmatrix} \right\}

Let

W = \langle S \rangle

be the span of

S

. Is the vector

\begin{bmatrix} -1 \\ 8 \\ -4 \end{bmatrix}

W

? Give an explanation of the reason for your answer.