Let e = {(x, y) e r2|xy > 0}. determine whether e is a subspace of r2 . x3

E is not a subspace of

Step-by-step explanation:

E is not a subspace of  

In order to see this, we must find two points (a,b), (c,d) in  E such that (a,b) + (c,d) is not in E.

Consider

(a,b) = (1,1)

(c,d) = (-1,-1)

It is easy to see that both (a,b) and (c,d) are in E since 1*1>0 and (1-)*(-1)>0.  

But (a,b) + (c,d) = (1-1, 1-1) = (0,0)

and (0,0) is not in E.

By the way, it can be proved that in any vector space all sub spaces must have the vector zero.

idk this answer sorry cant on this one.

step-by-step explanation:

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step-by-step explanation: