Question

Decide whether the set S is a linearly independent subset of the given vector space V.
V=R^3 S=([2,-1,4],[4,-2,8])

Answer 1

[2,-1,4] = (1/2) (4,-2,8] . So no. S only span a line in R^3

Answer 2

how did you get 1/2?

Answer 3

so its dependent?

Answer 4

Yes the vectors are dependent since one of them is a scalar multiple of the other one

Answer 5

You can view it in either way:
[2,-1,4] = (1/2)* [4,-2,8]

or

(2)*[2,-1,4] = [4,-2,8]