Let (

V;+; ) be R3 with the usual vector addition and scalar multiplication. For each of

the following, either use the subspace test to show that the given W is a subspace of (V;+; )

or explain why W is not a subspace.

(i) W := {(x1; x2; x3) eV |x1 + x2 -x3 = 0}.

(ii) W := {(x1; x2; x3) eV |x1 + x2 -x3 = 1}.

(iii) W := {(2t; 3t -1;-t) |t eR}.

(iv) W := {(2t; 3t;-t) |t eR}.

i) W is a subspace, not 100% sure on my working

ii) since 0 vector not included, its not a subspace

iii) Not sure where to start.

iv) Not sure where to start.

I've re-read all my course material over and over but i just need some worked through solutions to get to grips with it. Any help would be much appreciated.

Thanks