Exercise 3

Determine if each set is linearly independent in the natural space.

• (a)  $\{\hskip 1.00006pt\begin{pmatrix}1\\ 2\\ 0\end{pmatrix},\begin{pmatrix}-1\\ 1\\ 0\end{pmatrix}\hskip 1.00006pt\}$     (b)  $\{\hskip 1.00006pt(\begin{matrix}1&3&1\end{matrix}),(\begin{matrix}-1&4&3\end{matrix}),(\begin{matrix}-1&11&7\end{matrix})\hskip 1.00006pt\}$     (c)  $\{\hskip 1.00006pt\begin{pmatrix}5&4\\ 1&2\end{pmatrix},\begin{pmatrix}0&0\\ 0&0\end{pmatrix},\begin{pmatrix}1&0\\ -1&4\end{pmatrix}\hskip 1.00006pt\}$