Linear algebra - please explain the following problem(p:268). dimensions of subspaces of R^3(R)?

see attached , it will clear your doubt..

clearly in W3 , x^2+y^2+z^2 = 0 iff x=y=z=0 so dim is 0 and in W4 for any value of x belongs to R , e^x always positive , so W4 is R3 and hence dimension of W4 is 3