A First Course in Linear Algebra · Problem SS.C41

Vectors — Robert Beezer

Mathematics — Linear Algebra · spanning-sets

Problem

Suppose that

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

. Let

W = \langle S \rangle

and let

\mathbf{y} = \begin{bmatrix} 5 \\ 1 \\ 3 \\ 5 \end{bmatrix}

. Is

\mathbf{y} \in W

? If so, provide an explicit linear combination that demonstrates this.