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

Question

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?

Answer 1

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

Solution for problem 19 Chapter 1.2

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

Chapter 1.2, Problem 19 is Solved