# Homework Help: Does a set of vectors span Rn

1. Oct 11, 2012

### testme

1. The problem statement, all variables and given/known data
Determine if the following sets of vectors span the indicated space

a) {[0 -6 -6], [8 -3 5], [-9 7 -2]}, ℝ3.
b) {[2 1 7 -2], [3 5 4 5], [4 -4 -3 -3], [-5 0 6 -4]}, ℝ4.

2. Relevant equations

3. The attempt at a solution
a) a[0 -6 -6] + b[8 -3 5] + c[-9 7 -2] = [x y z]
x = 8b - 9c
y = -6a -3b + 7c
z = -6a + 5b - 2c

I don't know where to go from here - I'm sure if I can figure that out I'll be able to do b as well.

2. Oct 11, 2012

### LCKurtz

Use row reduction.

3. Oct 11, 2012

### testme

We haven't been taught that yet that's why I'm not sure what he wants us to do..

We've been talking about linear independence, bases, and dimension but I don't know how I can go back and check if it spans the space.

4. Oct 11, 2012

### Zondrina

Have you been taught determinants? It would be much faster, but row reduction will give you the answer nicely.

5. Oct 11, 2012

### testme

No, we haven't really been taught how to do anything with matrices, except maybe adding matrices or multiplying matrices by a scalar.

6. Oct 11, 2012

### Zondrina

Google row reduction. There's lots of stuff out there and it really only takes 20-30 mins to learn once you've seen a few examples done.

EDIT : Here's a great explanation with an example :

Last edited by a moderator: Sep 25, 2014
7. Oct 11, 2012

### testme

Hmm, well, that helps, I think I can figure it out from here and I'll ask my professor if there was another method he expected us to know