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).
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!
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).