I think it helps to visualize the span of vectors and trace out what kind of space it fills out.
The span of two linearly independent vectors if visualized in a 3d space traces out a sheet or plane surface and that is probably why there is a plane surface in this slide.
keenan
Yes indeed. One important feature of the span not clearly illustrated by this slide is that the span of any set of vectors always contains the origin, which can be expressed as $0 \vec{u}_1 + \cdots + 0 \vec{u}_k$.
I think it helps to visualize the span of vectors and trace out what kind of space it fills out. The span of two linearly independent vectors if visualized in a 3d space traces out a sheet or plane surface and that is probably why there is a plane surface in this slide.
Yes indeed. One important feature of the span not clearly illustrated by this slide is that the span of any set of vectors always contains the origin, which can be expressed as $0 \vec{u}_1 + \cdots + 0 \vec{u}_k$.