Question

Linear algebra problem. Please help!

Determine whether or not W is a subspace of R^n

Answer 1

W is the set of all vectors in R4 such that
(x1)(x2)(x3)(x4)=0

Answer 2

so what is the question?

Answer 3

Determine whether or not W is a subspace of R^n

Answer 4

what is n?

Answer 5

Any dimension

Answer 6

Does that make sense?

Answer 7

no

Answer 8

n would be infinitude and that would be crazy
if you meant R^4 then the answer is NO

Answer 9

no, the book says R^n, meaning nth dimension. That information really doesn't affect the problem though

Answer 10

alright

Answer 11

W is not a linear subspace of R^4

Answer 12

right, but how did you arrive at that conclusion

Answer 13

pick two
(0,1,1,0) and (1,0,0,1)
add them and get (1,1,1,1)

Answer 14

So you mean by vector addition W fails to meet the requirement?

Answer 15

absolutissimo

Answer 16

oh because they have to equal 0, right?

Answer 17

since that is the condition imposed

Answer 18

right?

Answer 19

∀α,β∈ℝ,x,y∈W⇒(αx+βy)∈W, then W is a subspace

Answer 20

Okay I think I got it! Thanks man!