Can These Vector Sets Span Their Indicated Spaces?

[testme]

Homework Statement

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.

Homework Equations

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.

 

[LCKurtz]

Use row reduction.

 

[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.

 

[STEMucator]

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

 

[testme]

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

 

[STEMucator]

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

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 :

 

[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