## Determine Linearly Independent or Linearly Dependent. Express as a Linear Combination

## Problem 277

Determine whether the following set of vectors is linearly independent or linearly dependent. If the set is linearly dependent, express one vector in the set as a linear combination of the others.

\[\left\{\, \begin{bmatrix}

1 \\

0 \\

-1 \\

0

\end{bmatrix}, \begin{bmatrix}

1 \\

2 \\

3 \\

4

\end{bmatrix}, \begin{bmatrix}

-1 \\

-2 \\

0 \\

1

\end{bmatrix},

\begin{bmatrix}

-2 \\

-2 \\

7 \\

11

\end{bmatrix}\, \right\}.\]