QuestionLet $f: \mathbb{R} \rightarrow \mathbb{R}^{3}$ be defined by $f(x)=\langle 7 x, 4 x, 3-3 x\rangle$. Is $f$ a linear transformation? a. $$\begin{array}{l} f(x+y)=\square \\ f(x)+f(y)=\square+\square \end{array}$$
Does $f(x+y)=f(x)+f(y)$ for all $x, y \in \mathbb{R}$ ? choose $\square$ b. $$\begin{array}{l} f(c x)=\square \\ c(f(x))=\square(\square) \end{array}$$
Does $f(c x)=c(f(x))$ for all $c, x \in \mathbb{R}$ ? choose $\square$ c. Is $f$ a linear transformation? $\square$ choose