Prove Theorem 7. [Hint: For (a), compute , or prove (b)

Chapter 6, Problem 25E

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QUESTION:

Prove Theorem 7. [Hint: For (a), compute , or prove (b) first.]Reference Theorem 7:

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QUESTION:

Prove Theorem 7. [Hint: For (a), compute , or prove (b) first.]Reference Theorem 7:

ANSWER:

Solution 25EStep 1 of 3Suppose and are in .The matrix is an matrix with orthonormal columns. So is an orthogonal matrix with the property that .First prove part (b).Use the definition of dot product as follows: Therefore,

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