Question

Find all subsets of the set that forms a basis for R^3
S= {(1,3,2),(-4,1,1),(-2,7,-3),(2,1,1)}

Answer 1

Does anyone understand what to do? Cuz I don't

Answer 2

If I remember my lin. algebra class correctly, you just have to find the vectors that are linearly independent.

Answer 3

nooo they are not asking me if it is a basis

Answer 4

I have to find the subsets

Answer 5

Each set of vectors that are linearly independent with one another should form a basis of R^3.

Answer 6

ohhh so i wld play around using these 4 vectors?

Answer 7

Hi Samjordan, what do u want to know/ask in linear algebra???

Answer 8

LOL This question

Answer 9

I just remembered the other condition. Whatever vectors you pick to be in your subsets also need to span R^3. As far as I can tell, playing around with them would be the fastest, but you need at least 2 vectors in each subset.

Answer 10

I think I am getting it

Answer 11

sorry Sam, at present my knowledge on this topic is rusty !!

Answer 12

hehe ok hakirat Thanks for stoppiin by

Answer 13

no I think 3 vectors since it needs to be a basis

Answer 14

I think you're right.

Answer 15

I guess you wld take 3 vectors of the 4 and check if they are linearly dependant and then check another 3 and then another 3.... I am only assuming this

Answer 16

That would get the linearly independent factor taken care of, but then you would need to show that of those that are linearly independent, they also span R^3, and that's a little trickier to show.

Answer 17

One way you could do it is as such: Suppose you have a vector <x, y, x> in R^3. Then your set of vectors spans R^3 if you can find some combination of your vectors such that you can create the vectors <x+1, y, z>, <x, y+1, z>, and <x, y, z+1>.

Answer 18

Ok just processing it

Answer 19

okk wel that is liek showing the linear independance thingy

Answer 20

almost, but not quite. I'd suggest looking here for a better explanation. http://en.wikipedia.org/wiki/Basis_(linear_algebra)#Example_of_alternative_proofs

Answer 21

Just generalize their example to R^3

Answer 22

Thanks Kinggeorge

Answer 23

your welcome

Answer 24

Basis requires (1) span the space (2) are independent
a basis for R^3 consists of three linearly independent 3x1 vectors.
Dimension of the space = number of independent vectors needed to span it. So 3 for R^3

you have to check 4choose3 = 4 different subsets.
use elimination to show each set has 3 pivots (or not)