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Linear Algebra: A Geometric Approach - 2 Edition - Chapter 1.2 - Problem 19
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Solutions for Linear Algebra: A Geometric Approach | 2nd Edition | ISBN: 9781429215213 | Authors: Ted Shifrin, Malcolm Adams 9781429215213

Solution for problem 19 Chapter 1.2

a. Give an alternative proof of the Cauchy-Schwarz Inequality by minimizing the

Linear Algebra: A Geometric Approach | 2nd Edition


Problem 19

a. Give an alternative proof of the Cauchy-Schwarz Inequality by minimizing the quadratic function Q(t) = _x ty_2. Note that Q(t) 0 for all t . b. If Q(t0) Q(t) for all t , how is t0y related to x_? What does this say about projyx?

Accepted Solution
Step-by-Step Solution:

Step 1 of 3

To construct an alternative proof for the Cauchy Schwarz inequality.

Let us consider a quadratic function

                      (i).

It is noted that for all .

Now,

Chapter 1.2, Problem 19 is Solved

Step 2 of 3


Step 3 of 3

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a. Give an alternative proof of the Cauchy-Schwarz Inequality by minimizing the