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

**Chapter 1, Problem 19**

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**QUESTION:**

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?

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### Questions & Answers

**QUESTION:**

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:**

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,