Prove that if W is a subspace of Rn then W WSolutionLet u be

Prove that if W is a subspace of R^n, then (W^)^= W.

Solution

Let u be an arbitary element of (W)   and let v be an arbitrary element of W . Then u.v = 0 so that        u W. Hence (W)    W.

Now, let w be an arbitrary element of W. Then w.v = 0. This implies that w (W) .Hence, W (W)   

Thus, (W) =  W