Glossary

To add vectors given in component form, we add each component separately. For instance, $\begin{pmatrix} 1 \\ 2 \end{pmatrix} + \begin{pmatrix} 4 \\ 3 \end{pmatrix} = \begin{pmatrix} 1 + 4 \\ 2 + 3 \end{pmatrix} = \begin{pmatrix} 5 \\ 5 \end{pmatrix}.$
Vector addition is commutative, meaning that $\mathbf{a}+\mathbf{b} = \mathbf{b}+\mathbf{a}.$