# Linear Algebra: Geometric Description of Span

1. Aug 25, 2007

### Dan C

1. The problem statement, all variables and given/known data
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, a$$V_{1}$$ + b$$V_{2}$$ = a$$V_{1}$$ +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.

2. Aug 25, 2007

### 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.

Last edited: Aug 25, 2007