Identifying Redundant Vectors from a 1x4 Matrix

[Derill03]

im given four vectors as a 1x4 matrices:

[1,4,2,8]^t = v1
[2,5,3,9]^t = v2
[11,14,12,18]^t = v3
[4,3,2,1]^t = v4

How can i know which if any of these vectors can be removed without changing the span?

 

[dx]

Check if they're linearly independent. If they are, then you cannot remove any of them without changing the span.

 

[Derill03]

How can i tell if the vectors are a basis for R^4?

 

[HallsofIvy]

A basis for an n dimensional vector space has three properties
1) the vectors span the space
2) the vectors are independent
3) the set contains n vectors

and, any two of those is sufficient to prove the third.

You know you have four vectors here. If they are independent, then they must also span the space and are a basis. If they are not independent, they do not form a basis.