3. Determine if each set given below is a basis for $\mathbb{R}^2$. Justify your answer.
(a) \{$\begin{bmatrix} 2 \\ 0 \end{bmatrix}$, $\begin{bmatrix} -4 \\ 9 \end{bmatrix}$\}
(b) \{$\begin{bmatrix} 1 \\ 1 \end{bmatrix}$\}
(c) \{$\begin{bmatrix} 1 \\ 0 \end{bmatrix}$, $\begin{bmatrix} 1 \\ 1 \end{bmatrix}$, $\begin{bmatrix} 2 \\ 3 \end{bmatrix}$\}
(d) \{$\begin{bmatrix} 1 \\ 1 \end{bmatrix}$, $\begin{bmatrix} -4 \\ -4 \end{bmatrix}$\}
(e) \{$\begin{bmatrix} 2 \\ -1 \end{bmatrix}$, $\begin{bmatrix} 3 \\ 5 \end{bmatrix}$\}
