The question is to determine whether the following vectors are linearly dependent or linearly independent.

The vectors are

{(1, 2, 3, 4), (2, 3, 4, 5), (3, 4, 5, 6), (4, 5, 6, 7)}

I put into matrix form and do gauss elimination on it

$\displaystyle

\left[ {\begin{array}{*{20}c}

1 & 2 & 3 & 4 \\

2 & 3 & 4 & 5 \\

3 & 4 & 5 & 6 \\

4 & 5 & 6 & 7 \\

\end{array}} \right]

$

$\displaystyle

= \left[ {\begin{array}{*{20}c}

1 & 2 & 3 & 4 \\

0 & 1 & 2 & 3 \\

0 & 0 & { - 1} & { - 2} \\

0 & 0 & 0 & 5 \\

\end{array}} \right]

$

$\displaystyle

= \left[ {\begin{array}{*{20}c}

1 & 0 & 0 & 0 \\

0 & 1 & 0 & { - 1} \\

0 & 0 & { - 1} & { - 2} \\

0 & 0 & 0 & 5 \\

\end{array}} \right]

$

From here I'm not sure how to intepret it, for whether it is dependent or independent. Answer say it is linearly dependent