Linear Algebra: Geometric Description of Span

[Dan C]

Homework Statement

Give a geometric description of the Span {V_{1},V_{2}} for the vectors V_{1} = [8, 2, -6]
and V_{2} = [12, 3, -9]

Those should be columns but I couldn't figure that out in latex, sorry.


2. The attempt at a solution

I have a solution, what I need help with is understanding it, this Span stuff just isn't clicking.

V_{2} = (3/2)V_{1}

So, aV_{1} + bV_{2} = aV_{1} +b(3/2)V_{2} = (a + (3b/2))V_{1}

So Span {V_{1}, V_{2}} is the set of points on the line through V_{1} and 0.


As I said I know the solution, but I don't understand it. I've reread the section on Span many times and I still don't know what exactly is going on. Any advice or help would be much appreciated.

 

[Dick]

You seem to understand it completely. The span is the subspace consisting of all vectors that are linear combinations of V1 and V2. And this subspace is the line through 0 and V1. There is not much I can add.