Let V be a vector space and S = { v1, ... , vn } a set of vectors from V.

1) What conditions do the vectors from S need to satisfy in order for them to form a basis for V ?

2) What would be the dimension of V in this case ?

3) Find the dimension and a basis for the linear subspace R^3 spanned by the vectors:

(3,-2,4) (1,-1,0) (3,-1,8)

4) Show that the vectors (1,1,0) (1,0,1) (0,1,1) form a basis for R^3

5) Find the components of the vector (3,4,5) in the basis considered in 4

this is no homework, this is a past exam papers without answers, i could really use this answers to revise, thank you in advance !