Suppose $f : \mathbb{R}^2 \to \mathbb{R}^2$ is a function and $f(\mathbf{a_n}) = \mathbf{b_n}$ for $n = 1, 2, 3$.

1. Does $\mathbf{a_3} = \mathbf{a_1} + \mathbf{a_2}$? choose yes no Does $f(\mathbf{a_3}) = f(\mathbf{a_1}) + f(\mathbf{a_2})$? choose yes no
2. Answer the following questions to determine whether $f$ is a linear transformation. Enter your answers as coordinate vectors of the form <1,2>.
   • $f(\mathbf{a_1}+\mathbf{a_2}) =$
   • $f(\mathbf{a_1}) + f(\mathbf{a_2}) =$ +
   • The function $f$ choose is definitely a linear transformation may or may not be a linear transformation cannot be a linear transformation . Be sure you can explain your answer.