LetUandVbe subspaces of a vector space W. Prove that their intersectionU∩Vis also a subspace ofW.

Printable View

- Oct 30th 2007, 01:04 PMpakmanSubspaces
Let

**U**and**V**be subspaces of a vector space W. Prove that their intersection**U**∩**V**is also a subspace of**W**. - Oct 30th 2007, 01:35 PMTKHunny
Get to work on that.

It is trivial to observe that the elements in the intersection are contained in the Vector Space.

You have three things to show:

1) There is a zero vector.

2) Closed for vector addition.

3) Closed for scalar multiplication.

Let's see how you do it. - Oct 30th 2007, 09:05 PMpakman
a*U(0) = a*U = 0

b*V(0) = b*V = 0

(U + V)(0) = U(0) + V(0) = 0 + 0 = 0

??? - Oct 30th 2007, 11:33 PMkalagota