Suppose U and W are finite-dimensional subspaces of an inner product space V. Prove that Pʊ Pw = 0 if and only if (u, w) = 0 for all u EU and all w Є W. Hint: By the equation PuPw = 0, we mean that for any vector v Є V, PUPwv = 0.

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4. Suppose U and W are finite-dimensional subspaces of an inner product space V. Prove
that Pu Pw = 0 if and only if (u, w) = 0 for all u Є U and all w =Є W.
Hint: By the equation PuPw = 0, we mean that for any vector v Є V, PUPwv = 0.
Transcribed Image Text:4. Suppose U and W are finite-dimensional subspaces of an inner product space V. Prove that Pu Pw = 0 if and only if (u, w) = 0 for all u Є U and all w =Є W. Hint: By the equation PuPw = 0, we mean that for any vector v Є V, PUPwv = 0.
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