(Solved): Determine whether the members of the given set of vectors are linearly independent. If they are li ...

Determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them. \[ \mathbf{x}^{(1)}=\left(\begin{array}{l} 5 \\ 5 \\ 0 \end{array}\right), \mathbf{x}^{(2)}=\left(\begin{array}{c} 0 \\ 25 \\ 25 \end{array}\right), \mathbf{x}^{(3)}=\left(\begin{array}{c} 5 \\ 10 \\ 5 \end{array}\right) \]