The span of vectors \(\Vect{s}_1,\dots ,\Vect{s}_r\) in \(\RNrSpc{n}\) is the collection of all those vectors \(\Vect{x}\) in \(\RNrSpc{n}\) which can be expressed as a linear combination of the vectors \(\Vect{s}_1,\dots ,\Vect{s}_r\):
| \(\SpanOfSet{ \Vect{s}_1,\dots ,\Vect{s}_r }\) | \(\DefEq \) | \(\SetSlct{ \Vect{x}\in\RNrSpc{n} }{ \text{there exist}\quad t_1,\dots , t_r\in \RNr \quad\text{for which}\quad \Vect{x}=t_1\Vect{s}_1+\cdots + t_r\Vect{s}_r }\) |