Question

Let T = { (x,y) | x,y are elements of real numbers ,x>=0, y>= 0} . Determine whether T is a subspace of a 2-dimensional vector space.

Answer 1

No, T is not a subspace.

T is not a vector space because if we take '+' as usual addition then its inverse does not exist in set T

Answer 2

To add to mohit.mangal's answer, T is not a subspace because it is not closed under scalar multiplication: If you take a vector (1, 2) that is in T, and multiply it by the negative number -3, you get a vector (-3, -6) that is not in T.