Question

INTERSECTION OF TWO SUBSPACES IS A SUBSPACE

Answer 1

First, since every subspace contains the zero vector (which, you may recall, is itself a subspace), at the very least, the intersection of two subspaces will contain the zero vector, and, hence will be a subspace.

Then, you just have to show that:
1.) For every vector "x" in \[V \cap W,\] the vector "kx" is also in the intersection of V & W (where k is scalar).

2.) For any two vectors x & y in the intersection of V & W, x + y is also in the intersection of V & W.

Is this at all helpful??

Answer 2

THANK U SIR