what-is-the-largest-value-of-the-quadratic-form-5-x_12-3-x_22-if-mathbfxt-mathbfx1

Question

What is the largest value of the quadratic form $5 x_{1}^{2}-3 x_{2}^{2}$ if $\mathbf{x}^{T} \mathbf{x}=1 ?$

Jack Chen · Answer

now in this problem, we have a restriction. So given x one square prospects to a square you close to one we want to mix mice. The following quadratic function five eggs, one square plus eight x to a square we want it makes my stays. But based on this restriction, we have this function. You goes to a five x one square past eight one minus x one square, which is eight minus Roeg&#x27;s one square since X Y score is known active, that is this functions place. So he goes to eight. And this equality holds when x y in close to zero, that is, X two equals to one. So this equation has a mixed more value. Eight. You will be achieved. It wouldn&#x27;t eggs. Wang, because of their next week, was the one.

Melissa Salvador · Answer

Okay, so we know that when we are, um, a square and something, we&#x27;re multiplying it by itself. So this would be xn minus one times X minus One is equal to Let&#x27;s distribute this right here to be X squared minus plan X. Now, let&#x27;s distribute on this stuff from the left because of the X squared minus X minus, X minus one or plus one. Sorry. And that is equal to X squared. Minus live. Next. What&#x27;s combine like terms? No. Let&#x27;s move this stuff from the right to do a left. We&#x27;re gonna be subtracting X squared. We&#x27;re gonna be at any five X. Okay, this goes away. This goes away. The X squared goes away, too. And we&#x27;re left with three expos. Want these people to syrup? Let&#x27;s move that one over to the other side. Native one. Divide like dream. Get the X less than equal to and 1/3. And so that way there is our answer

Ankit Gupta · Answer

we have a soul. Extra de power five plus Xs Square is greater than equal to X cubed plus toe. We subtract two x cubed and drew from both sides. We get actually power fire minus two x cubed plus X. A square minus two is greater than +10 We take extra. The power three a department from we get excess square minus two plus one, multiplied by X squared minus two is greater than equal to zero. This can very Internet access where my next to multiplied by x cubed plus one is greater than equal to zero. This can return as explosive square otaku multiplied by X minus. The square root off to multiplied by X plus one multiplied by X X square plus X plus. One is greater than equal to zero. This is always a possibility for anywhere blew off X so we can divide by this integral sides and the sign Open equality will not change. We get explosives square root up to multiplied by X minus. The square Oto, former player by X plus one is greater than equal to zero. We represent all the critical points. It means the square root toe minus one minus X squared. Talked. We start with Palestine from the writer incident in the Sinai. Alternatively, we get XB launched Toe lodge interval minus Esquire. Auto miners When the union closure in trouble. Square it off. Toto Infinity! This is the sort. Isn&#x27;t off this inequality?

Noraney Ocampo · Answer

So they&#x27;re telling you that the equation expe you&#x27;d less site x square. It&#x27;s weird. War equals defy, has an answer or has a solution that is between Cyril and one. So you&#x27;re gonna make a table to find the answer, and you&#x27;re going around it to the nearest tent. So I did the table. Let me share it with you. It&#x27;s notice. Yes, there is a solution between Syria and one you wanted to be 50 gives you four and one gives you 10. So five has to be somewhere in between. And since they want the answer to the nearest sense, you could put all the tense places in between. So you have syrup in 13 point to certain three that you can find the one that gives you the best or the process answer to five. And the closest answer to five. In this case, let me see if I don&#x27;t point for it gives you 4.8. If I do 0.5 against 5.37 so I could do for Sarah 0.45 in the craft so I could see whether it&#x27;s closer. My 0.4 or 2.5 So if I do 0.45 piece to me. Point 10 5.10. Let me do this one so that I can share them with you. So please six. So let me at a picture that I took off Newest one. And notice that surplus 43 gives me closer to five and then surprise 45 this bigger. So then you are going to go close to the nearest 10th. Would be syrup on for this. The three is going around at the 45 is so a little bit higher the 46 iss higher on the point like this even higher. So, sir, pulling four is closer when you&#x27;re out it to the nearest tent. Because if you choose, you&#x27;re from a number has to be way smaller than five. So then it&#x27;s gonna make your 10th place wrong 2.4 grown down instead of running up. So your ex one of your answers be necks is close. So zero point for

Ankit Gupta · Answer

we have to solve excess square minus X minus five. Greater than equal to X minus two. We subtract. Explain both sides and a tow from both sides. Vigor. Excess square minus two x minus. Terry is greater than equal to zero. Defect tries this we get X square minus terry X plus X minus. Terry is greater than equal to zero. It implies that X multiplied by X minus three plus one multiplayer by X minus three is greater than equal to zero. It implies that X minus terry multiplied by X plus one is greater than equal to zero. V Represent the critical points on the number line. It means, except military and X equal to minus one is we start with plus in from the right hand side intended saying, Alternatively, we get this. Now that&#x27;s Alderson off. This iniquity is X belongs to minus infinity to minus one. Closed in Travel Union three to Infinity

Problem

In Exercises 21 and $22,$ matrices are $n \times …

Problem 20 Medium Difficulty

What is the largest value of the quadratic form $5 x_{1}^{2}-3 x_{2}^{2}$ if $\mathbf{x}^{T} \mathbf{x}=1 ?$

Answer

5
-3

Related Courses

Linear Algebra and Its Applications

Related Topics

Discussion

Top Algebra Educators

Catherine R.

Anna Marie V.

Heather Z.

Michael J.

Algebra Courses

Absolute Value - Example 1

Absolute Value - Example 2

Recommended Videos

Watch More Solved Questions in Chapter 7

Video Transcript

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

Catherine R.

Anna Marie V.

Heather Z.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

5-3

Linear Algebra and Its Applications

Catherine R.

Anna Marie V.

Heather Z.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Catherine R.

Anna Marie V.

Heather Z.

Michael J.

5
-3

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications