Question

The intersection of two subspaces of a vector space V(f) is a subspace of V

Answer 1

To prove that the intersection U∩V is a subspace of Rn, we check the following subspace criteria:

The zero vector 0 of Rn is in U∩V.

For all x,y∈U∩V, the sum x+y∈U∩V.

For all x∈U∩V and r∈R, we have rx∈U∩V.

As U and V are subspaces of Rn, the zero vector 0 is in both U and V.

Hence the zero vector 0∈Rn lies in the intersection U∩V.

So condition 1 is met.

Answer 2

Answer:

Prove that the intersection of any two subspace of a vector space V(f) is also a subspace of v(f).