Question: show that the set L={(x,y,z,w) is in | x+y-z+w=0} with operations from is a vector space.

Answer: show that it's closed under vector addition (between itself and an arbatrary vecotr) and closed under scalar multiplication (between itself and an arbitrary constant)

Confusion: I thought that's what's done to show something is a subspace? To show something is a vector space, the set must satisfy 10 properties including things like

foruandvin the vector space

and

so why is it in the answer they only showed that it was closed under scalar multiplication and vector addition and didn't need to show the other properties, for example like the two I list above?