Hi

I have to check as this vectors are linear dependent?

My calculation says no, they are linear independent because every coefficient in the linear combination is zero but I don't know as I did my work well. Could you say yer or no to my answer?

The Vectors are in $\displaystyle \mathbb{R}^{4}$

$\displaystyle \begin{pmatrix}1 \\ 3 \\ 2 \\0 \end{pmatrix}, \ \begin{pmatrix}-2 \\ -1 \\ 0 \\3 \end{pmatrix}, \ \begin{pmatrix}5 \\ -2 \\ 4 \\5 \end{pmatrix}, \ \begin{pmatrix}0 \\ 1 \\ 3 \\5 \end{pmatrix}$