For any two subspaces of an inner product space..

Prove that for any two subspaces W_{1} and W_{2 }of an inner product space V, we have

a) (W_{1} + W_{2})^⊥ = W_{1}^⊥ ∩ W_{2}^⊥ and

b) (W_{1} ∩ W_{2})^⊥ = W_{1}^⊥ + W_{2}^⊥

Hint: The second follows from the first- you may use the fact that (W^⊥)^⊥ = W.

Any help would be greatly appreciated!

Re: For any two subspaces of an inner product space..

Hey TimsBobby2.

Hint: The perpendicular space of W1 + W2 will not include anything that spans along that space (figure out the plane that spans the two spaces and get the perpendicular space of that).