Question

whats is span? how can spaning a vector?

Answer 1

span is how far it can reach

Answer 2

in a plane, we only need 2 vectors that are not parallel in order to reach every point on the plane .... <1,0> and <0,1> tend to be these vectors for a standard xy plane

Answer 3

Let\[S=\left\{ \vec v_1,\vec v_2,\dots,\vec v_n \right\}\]be s set of vectors in a vector space V, and W be the set of all linear combinations of v1, v2,..., vn.

Then W is the span of the vectors v1, v2,..,vn and is denoted by\[W=\text{span}(S)\]or\[W=\text{span}\left\{ \vec v_1,\vec v_2,\dots,\vec v_n \right\}\]and it is said that the vectors\[\left\{ \vec v_1,\vec v_2,\dots,\vec v_n \right\}\]span W