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Proof Let u and v be nonzero vectors in an innerproduct space V. Prove that u projvu is

Chapter 5, Problem 90

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QUESTION:

Proof Let \(\mathbf{u}\) and \(\mathbf{v}\) be nonzero vectors in an inner product space V. Prove that \(\mathbf{u}- proj_{\mathbf{v}} \mathbf{u}\) is orthogonal to \(\mathbf{v}\).

Text Transcription:

u

v

u -  proj_{v} u

Questions & Answers

QUESTION:

Proof Let \(\mathbf{u}\) and \(\mathbf{v}\) be nonzero vectors in an inner product space V. Prove that \(\mathbf{u}- proj_{\mathbf{v}} \mathbf{u}\) is orthogonal to \(\mathbf{v}\).

Text Transcription:

u

v

u -  proj_{v} u

ANSWER:

Step 1 of 3

Proof Let  and  be nonzero vectors in an inner product space . Prove that   is orthogonal to .

By definition, if  is orthogonal to  then

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