$2 v=\left[\begin{array}{l}2 v_{1} \\ 2 v_{2}\end{array}\right]=v+v \qquad\pm cv=\left[\begin{array}{l}\pm cv_{1} \\ \pm cv_{2}\end{array}\right]$ **Scalar Multiplication** for [[Vector|vectors]] applies the [[scalar]] to each component of the vector. By definition, the scalar and the component are of the same field, so their multiplication is defined.