Let$\displaystyle L: R^{2}->R^{2} $be the linear transformation defined by $\displaystyle L(\begin{pmatrix}a_{1}\\a_{2}\end{pmatrix})=\begin {pmatrix}1&2\\2&4\end{pmatrix}\begin{pmatrix}a_{1} \\a_{2}\end{pmatrix}$

a) Is $\displaystyle \begin{pmatrix}1\\2\end{pmatrix}$ in ker L?

b) Is $\displaystyle \begin{pmatrix}2\\-1\end{pmatrix}$ in ker L?

c) Is $\displaystyle \begin{pmatrix}3\\6\end{pmatrix}$ in range L?

c) Is $\displaystyle \begin{pmatrix}2\\3\end{pmatrix}$ in range L?

Thank you for your help!