Suppose that W1 and W2 are subspaces of V and dimW1<dimW2. Prove that there is a...

Suppose that W1 and W2 are subspaces of V and dimW1<dimW2. Prove that there is a nonzero vector in W2 which is orthogonal to all vectors in W1.

Expert Solution

Here I provide two proof. The first proof is little in size and as it uses inequality so this proof is valid only when V is finite dimensional wheather the second proof is general, for both finite and infinite dimension.

Colby Messinger answered 2 years ago

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Suppose that W1 and W2 are subspaces of V and dimW1<dimW2. Prove that there is a...

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