To add vectors given in component form, we add each component separately. For instance, \[ \begin{pmatrix} 1 \\ 2 \end{pmatrix} + \begin{pmatrix} 4 \\ 3 \end{pmatrix} = \begin{pmatrix} 1 + 4 \\ 2 + 3 \end{pmatrix} = \begin{pmatrix} 5 \\ 5 \end{pmatrix}. \]
Graphically, this is equivalent to taking the lines representing each vector and placing them end to end.
Vector addition is commutative, meaning that \[\mathbf{a}+\mathbf{b} = \mathbf{b}+\mathbf{a}.\]
