Question

let S and T be subspaces of a vector space V. Prove that S intersect T is also a subspace of V

Answer 1

All you need to do is take your conditions for Vector Spaces (Closure, Associativity, Identity, Multiplication by a scalar etc.) and show that if it's true for S and T, it's also true for the intersect of S and T.

Answer 2

since S and T are Vspaces they intersect at 0 to begin with

Answer 3

I know its good for planar sets

Answer 4

3ds intesect in planes; 4d intesect in spheres etc

Answer 5

but then S and T dont even have to be R^equal do they