subspaces

H is not a subspace since for c < 0, then c(2x, 0) = (2cx, 0) which is not in H as 2cx < 0

Recall that H is a subspace iff for A, B in H, then A + B and cA must be in H, where c is any scalar (either in R or C)

Y is also not a subspace
since for Y1 = (a+2b+1, a+3b) Y2 = (c+2d+1, c+3d)
Y1 + Y2 = ((a+c) + 2(b + d) + 2, (a + c) + 3(b + d))
but the resultant form does not fit the definition of Y.