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