(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Give a geometric description of the Span {[tex]V_{1}[/tex],[tex]V_{2}[/tex]} for the vectors [tex]V_{1}[/tex] = [8, 2, -6]

and [tex]V_{2}[/tex] = [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.

[tex]V_{2}[/tex] = (3/2)[tex]V_{1}[/tex]

So, a[tex]V_{1}[/tex] + b[tex]V_{2}[/tex] = a[tex]V_{1}[/tex] +b(3/2)[tex]V_{2}[/tex] = (a + (3b/2))[tex]V_{1}[/tex]

So Span {[tex]V_{1}[/tex], [tex]V_{2}[/tex]} is the set of points on the line through [tex]V_{1}[/tex] 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Linear Algebra: Geometric Description of Span

**Physics Forums | Science Articles, Homework Help, Discussion**