Chapter 4.2, Problem 47E

Proof Complete the proof of the cancellation property of vector addition by justifying each step.

Prove that if $u$, $v$, and $w$ are vectors in a vector space $V$ such that $u+w=v+w$, then $u=v$.

$\begin{array}{rll}u+w& =& v+w\\ u+w+\left(-w\right)& =& v+w+\left(-w\right)\text{a}.\underset{\_}{}\\ u+\left(w+\left(-w\right)\right)& =& v+\left(w+\left(-w\right)\right)\text{b}.\underset{\_}{}\\ u+0& =& v+0\text{c}.\underset{\_}{}\end{array}$

$u=v\text{d}\text{.\_\_\_\_}$