Vectors and geometry

Vectors add and scale componentwise. Picture: arrows placed head to tail.

Standard basis: $(3, -1, 2) = 3\mathbf{e}_1 - \mathbf{e}_2 + 2\mathbf{e}_3$.

Linear combination: $\lambda_1\mathbf{v}_1 + \cdots + \lambda_k\mathbf{v}_k$ — the central idea of the course.