Multiplying an argument to a linear transformation

Question

A property of linear transformations $L$ is that $L(cu)=cL(u)$ for any $u∈V$ and $c\in\mathbb R$.

Suppose $u=[u_1, u_1^2]$. Is $L(cu) = [cu_1, c^2u_2^2]$ or $[cu_1, cu_2^2]$?

Answer 1

$L(cu)=[cu_1,cu_2^2]$. When multiplying a vector that goes through a linear transformation, ignore the content of the vector and simply multiply each component by the given factor.