{(x,y)^T I x=3y} determine whether the set forms a subspace of R^2?

Question

^T is transpose

Answer 1

To be a subspace, it has to behave in the proper ways under the proper operations (addition, multiplication by scalars). Obviously, it does.

So the only things you have to check are:

A. Is the identity element in there?
B. For every member, is the additive inverse in there?
C. For any two members, is their sum in there?
D. For any member and any scalar, is the scalar multiple of the element in there?

Each of those properties is easy to prove true, via very simple algebra.

So yes, it's a subspace.

Answer 2

You must be that real smart guy who makes me feel extremely dumb. I'm glad they're people like you who probably are responsible for creating prescription drugs to keep us well, among millions of other amazing developments. I do hope you use your genius brain for important & benefical purposes. Good Luck