Exercise 2

Decide if each is a basis for $\mathbb{R}^{3}$.

• (a)  $\langle\begin{pmatrix}1\\ 2\\ 3\end{pmatrix},\begin{pmatrix}3\\ 2\\ 1\end{pmatrix},\begin{pmatrix}0\\ 0\\ 1\end{pmatrix}\rangle$     (b)  $\langle\begin{pmatrix}1\\ 2\\ 3\end{pmatrix},\begin{pmatrix}3\\ 2\\ 1\end{pmatrix}\rangle$     (c)  $\langle\begin{pmatrix}0\\ 2\\ -1\end{pmatrix},\begin{pmatrix}1\\ 1\\ 1\end{pmatrix},\begin{pmatrix}2\\ 5\\ 0\end{pmatrix}\rangle$     (d)  $\langle\begin{pmatrix}0\\ 2\\ -1\end{pmatrix},\begin{pmatrix}1\\ 1\\ 1\end{pmatrix},\begin{pmatrix}1\\ 3\\ 0\end{pmatrix}\rangle$