subspace & dimension

[passionatekiss]

Show that if U and V are subspaces of R^n and U intersect V = {0}, then dim(U+V)=dimU + dimV.

U+V = {z|z=u+v where u in U and v in V}

 

All I know is the two vectors U and V pass through the origin. ie. they intersect at 0, origin.

 

How do I go about it? Thank you.