# Subspaces; Linear span

1. Jun 22, 2009

### dracolnyte

1. The problem statement, all variables and given/known data
(i)Show that the linear span of the vector a1 = (-7, 8, 5) is the line whose equation is
x/(-7) = y/8 = z/5

3. The attempt at a solution
The problem is, I don't know where or how to start.

2. Jun 22, 2009

### Dick

Define the 'linear span of a vector'. Look it up if you have to.

3. Jun 22, 2009

### dracolnyte

The linear span of a vector is the collection of all linear combinations of the vectors a1, a2..., ak

4. Jun 22, 2009

### Dick

Ok, so for one vector v1 it's the set of all vectors k*v1 for k any real number, right?

5. Jun 23, 2009

### dracolnyte

Ya, and then?

6. Jun 23, 2009

### Dick

You are supposed to be helping here. Guess. (x,y,z) is a point in the span of (-7, 8, 5). What's it equal to?

7. Jun 23, 2009

### dracolnyte

Okay so
-7k = x
8k = y
5k = z

8. Jun 23, 2009

### dracolnyte

Got it, thank you so much. I'll be back with more for sure lol.