## Find a Basis for the Subspace spanned by Five Vectors

## Problem 709

Let $S=\{\mathbf{v}_{1},\mathbf{v}_{2},\mathbf{v}_{3},\mathbf{v}_{4},\mathbf{v}_{5}\}$ where

\[

\mathbf{v}_{1}=

\begin{bmatrix}

1 \\ 2 \\ 2 \\ -1

\end{bmatrix}

,\;\mathbf{v}_{2}=

\begin{bmatrix}

1 \\ 3 \\ 1 \\ 1

\end{bmatrix}

,\;\mathbf{v}_{3}=

\begin{bmatrix}

1 \\ 5 \\ -1 \\ 5

\end{bmatrix}

,\;\mathbf{v}_{4}=

\begin{bmatrix}

1 \\ 1 \\ 4 \\ -1

\end{bmatrix}

,\;\mathbf{v}_{5}=

\begin{bmatrix}

2 \\ 7 \\ 0 \\ 2

\end{bmatrix}

.\]
Find a basis for the span $\Span(S)$.