- #1
M55ikael
- 17
- 0
Hi!
I can't for the life of me figure out how to do this. I need to find the basis for the span of these four vectors:
V1= 3, 1, -2, -4
V2 = -5, -3, 5, 9
V3 = 5, -1, 0, -2
V4 = -1, 5 -6 -8
2. The attempt at a solution
I've figured out that the determinant is zero, so in its current form it's definitely not a basis. At least one of the vectors are obsolete, and they don't span R4. I was going to take away a vector at random and see if the remaining vectors were linearly dependant or not, but I'm not sure how to prove that a non square matrix is linearly independent.
Example: Say I take away one vector and use gauss-jordan elimination on the matrix comprised of the remaining vectors. I would eventually end up with all the constants equal to zero, or one or more rows of zeros. But if I ended up with an identity matrix, it wouldn't actually prove that the ONLY solution was that alle the constants are zero, would it?
This is my first post , so please be kind ;-) Thanks for helping me out!
EDIT: Sorry, this might have been better suited for the physics sub-forum.
Homework Statement
I can't for the life of me figure out how to do this. I need to find the basis for the span of these four vectors:
V1= 3, 1, -2, -4
V2 = -5, -3, 5, 9
V3 = 5, -1, 0, -2
V4 = -1, 5 -6 -8
2. The attempt at a solution
I've figured out that the determinant is zero, so in its current form it's definitely not a basis. At least one of the vectors are obsolete, and they don't span R4. I was going to take away a vector at random and see if the remaining vectors were linearly dependant or not, but I'm not sure how to prove that a non square matrix is linearly independent.
Example: Say I take away one vector and use gauss-jordan elimination on the matrix comprised of the remaining vectors. I would eventually end up with all the constants equal to zero, or one or more rows of zeros. But if I ended up with an identity matrix, it wouldn't actually prove that the ONLY solution was that alle the constants are zero, would it?
This is my first post , so please be kind ;-) Thanks for helping me out!
EDIT: Sorry, this might have been better suited for the physics sub-forum.
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