Chapter 6.1, Problem 1TFR

True-False Review

For Questions (a)-(f), decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem from the text. If false, provide an example, illustration, or brief explanation of why the statement is false.

A linear transformation $T:V\to W$ is a mapping that satisfies the conditions $T\left(u+v\right)=T\left(u\right)+T\left(v\right)$ and $T\left(c\cdot v\right)=c\cdot T\left(v\right)$ for some vectors $u$, $v$ in $V$ and for some scalar $c$.