The <linear span> is $\{\lambda\mathbf a+\mu\mathbf b:\lambda,\mu\in\mathbb R\}$, a <vector subspace> of $\mathbb R^3$. Its <dimension> is \b[zero] if both vectors vanish, \b[one] if at least one is nonzero and they are <linearly dependent>, and \b[two] if they are <linearly independent>. The corresponding geometric sets are the origin, a line through the origin, and a plane through the origin.

Solution

Past exam of the mathematical methods I course of the University of Oxford / 2021 / 8 / a / i / Solution

 Solution (source code)