Can These Vector Sets Span Their Indicated Spaces?

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Homework Help Overview

The discussion revolves around determining whether specific sets of vectors span their respective vector spaces, ℝ3 and ℝ4. The original poster presents two sets of vectors and expresses uncertainty about how to proceed with the problem.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss various methods for checking if the sets span the indicated spaces, including row reduction and determinants. The original poster questions how to apply these methods given their current understanding of linear independence and matrix operations.

Discussion Status

Some participants suggest using row reduction as a method, while others note that the original poster has not been taught this technique yet. There is a recognition of the need for clarification on the methods available to the original poster, and they express intent to seek further guidance from their professor.

Contextual Notes

Participants mention that the original poster has only been taught basic operations with matrices, which may limit their ability to apply more advanced techniques for determining span.

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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.
 
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Use row reduction.
 
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.
 
Have you been taught determinants? It would be much faster, but row reduction will give you the answer nicely.
 
No, we haven't really been taught how to do anything with matrices, except maybe adding matrices or multiplying matrices by a scalar.
 
testme said:
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 :
 
Last edited by a moderator:
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
 

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