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Let _ be the line spanned by a R2, and let R_ : R2 R2 be the linear map defined by

Linear Algebra: A Geometric Approach | 2nd Edition | ISBN: 9781429215213 | Authors: Ted Shifrin, Malcolm Adams ISBN: 9781429215213 438

Solution for problem 9 Chapter 2.2

Linear Algebra: A Geometric Approach | 2nd Edition

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Linear Algebra: A Geometric Approach | 2nd Edition | ISBN: 9781429215213 | Authors: Ted Shifrin, Malcolm Adams

Linear Algebra: A Geometric Approach | 2nd Edition

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Problem 9

Let _ be the line spanned by a R2, and let R_ : R2 R2 be the linear map defined by reflection across _. Using the formula R_(x) = x_ x given in Example 3, verify that a. _R_(x)_ = _x_ for all x R2. b. R_(x) a = x a for all x R2; i.e., the angle between x and _ is the same as the angle between R_(x) and _.

Step-by-Step Solution:
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Generalized Principle of Counting  If ‘r’ experiments are to be performed, where ‘n’ represents the number of outcomes for an experiment, then the total number of outcomes is expressed by the following: ◦ n 1* n 2* … * n r  Example(s) ◦ Suppose a car comes with 5 different colors, 3 different models, dealer protection potential, and leather...

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Chapter 2.2, Problem 9 is Solved
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Textbook: Linear Algebra: A Geometric Approach
Edition: 2
Author: Ted Shifrin, Malcolm Adams
ISBN: 9781429215213

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Let _ be the line spanned by a R2, and let R_ : R2 R2 be the linear map defined by

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