Question

Is W a subspace of V?
W=(x,y,2x-3y)
V=R^3

Answer 1

They are closed under addition:\[(x_1,y_1,2x_1-3y_1)
+(x_2,y_2,2x_2-3y_2)\]\[=(x_1+x_2,y_1+y_2,2(x_1+x_2)-3(y_1+y_2))\]which is in W
I'll let you verify that there is nothing to multiply it by that would take it out of W either, hence it is also closed under scalar multiplication

Answer 2

Thanks That was clear :D