5

[12] Za_ Jet " =44,4,2,-3,0) . Find all szalars such that Iml-s.Veriily tha Cauchy Schwanz Inequality holds for #=41,2-16=06,4.2) In %'...

Question

[12] Za_ Jet " =44,4,2,-3,0) . Find all szalars such that Iml-s.Veriily tha Cauchy Schwanz Inequality holds for #=41,2-16=06,4.2) In %'

[12] Za_ Jet " =44,4,2,-3,0) . Find all szalars such that Iml-s. Veriily tha Cauchy Schwanz Inequality holds for #=41,2-16=06,4.2) In %'



Answers

Use Theorem 3 to prove the Cauchy-Schwarz Inequality:

$$
\mid a \cdot b \mid \le \mid a \mid \mid b \mid $$

In this question. Were you calling about the equation? Drowned where we have the normal the They crossed W square the way, coach. You know, the normal V square times the normal W square, minus the VW Square. And now from here we can write. We talked up in your square. It will be equal to the no on the V Square times the normal W square minus the norm on the V cross w square. From here, we can say that the V W square. If we remove this quantity here, it will be Ah, Big Miss. Smaller than equal Jew. Mhm, mhm the norm on the V Square times, the nominal w square. And then we do the square root on both sides. We sink in the V cause we docked up in you. Absolutely. Leo will be smaller. ICO do the norm under V square times the normal w square. And this one is known as a coach e squat inequality

So here we want to prove the Kashi Swartz inequality which is the fact that U dot v. The magnitude that is going to be western or equal to the magnitude of you and the magnitude of B. Well keep in mind that when we have U dot V yeah that is going to be equal to um the magnitude of you. I'm the magnitude of you times cosign theta. Well what do you know about code something? We'll consider the graph of codes in X. What is the greatest value that code syntax can be? I will go to radiance but you see the greatest value that coastline X can be is one. Um So if the greatest value could possibly be is one, what's the greatest this value can be? Well the greatest it could be is um the magnitude of U. Times the magnitude of V. So we see it's always going to be less than or equal to that.

In the problem. We have a lot more be because Peter So two down three in the boot, it becomes minus more Iman. Be this great listening who weighed on me And this is a level equal to mourn A to be We know this is my last one is the lesson, people, Because this is listening. This gives us our desire. So listen by no the same that we, uh have you the statement in the farm more. Hey, don't be so we're not be lesson with more. A more B. This is the answer to the human.

Children. Three stairs there. Hey, don't be executed. Magnitude of here. Magnificent B because his tavern Twitter is angle between and p oh, on taking absolute well on both. I figured you don't be. Is the cradle Mhm? Yeah. Off key called. Come on, I think Yeah. Off the off course. Yeah, 35. Okay. Mhm. And it. Yeah, yeah, yeah. Mhm, yeah. Means off. Prosecutor has vanish. One, 21 parent Because it absolutist less cynical one. Therefore, you don't be and so we don't hear in tow. Absolutely cost Utah since cost you guys, This is a Senate goto one. So a dog pee anything. This thing called the magnitude of being magnet. Well, this is called cheap. So what indignity?


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