exercises-3-8-refer-to-mathbbp_2-with-the-inner-product-given-by-evaluation-at-10-and-1-see-exampl-5

Question

Exercises $3-8$ refer to $\mathbb{P}_{2}$ with the inner product given by evaluation at $-1,0,$ and $1 .$ (See Example $2 . )$
Compute $\|p\|$ and $\|q\|,$ for $p$ and $q$ in Exercise 4

Angelo Rendina · Accepted Answer

let me dinner with X. Why the vectors containing the permits? P and cute computer T minus 10 and one. So x is the vector minus 40 in two. And why is the Vector 535 now? The length off being with respect to this particular in a product is given by the root office in their product be against me. And by definition of the inner product report for Polly Normals, this is X Durex. What X is a vector we&#x27;ve completed previously? Now this is the route off. Well, four square plus two square. So that&#x27;s 20 out of 20. Similarly, the length off cue is the root off que against you, which is, by definition again off the product between Polly Normals route off. Why that wine were wise. The victor we have to find up there and again. This is route off 59

Angelo Rendina · Answer

to simplify the notation. Let me then all with axe. The factor with the polynomial peed computer T minus one in zero and in one. So if you replace T with these values, you get that be evaluated minus 10 and one is minus 40 and two. I mean the same with why which contains the values off cue evaluated in minus 1011 So that turns out to be 53 and five. Now the inner product off the perimeter p against a pole in a queue is by definition the dot product between X and y, as we&#x27;ve put it here and therefore is minus 20 plus zero plus 10 which is minus Stan.

Angelo Rendina · Answer

so, accent, Why they&#x27;re not the vectors containing the binomial speed and cue computer in minus 101 So, actually, the vector minus 40 in two. And why is the Vector 535? Now we&#x27;re asked to compute the projection on topi off cue, we call the definition of projection that Xena product off cue against B dividing in a product off be against B. And this number multiplies the vector p No, because of the definition of innit? Prague between Polly Normals. We know that didn&#x27;t probably between Q and P is why Durex and the inner product be against B is extra X and everything multiplies the bulletin. Opie. Now why the X we see is just minus Stan. An extra tax used 20 and his number multiplies be. And so all in all the protection off cue on Toby. He&#x27;s minus one house. Me

Fuzail Shakir · Answer

Okay, so here have a one is equal to p. B. One is equal to negative. P C one is equal to two p A to is equal to two. Q B two is equal to Q and see two is equal to negative. Q. So ADA is P Times to cube, plus negative p. Times Q plus two p times negative cute, which is equal to negative P. Q.

Brian Austin · Answer

for this question, we&#x27;re going to evaluate the expression three p minus two Q plus nine when P equals Ain&#x27;t in cubicles negative to all we&#x27;re going to do is substitute in the value for each variable given into the corresponding variable. So P equals eight. We&#x27;re gonna plug in here for P so three times a day and then Q equals negative, too. We&#x27;re gonna plug in here for Q so negative two times negative, too. And then we&#x27;re just gonna evaluate the expression. Multiplication comes first in this expression. So doing the multiplication. Here we get three times eight, which is 24 and the negative two times negative, too, which is positive for and then bringing down the last night. Now adding everything together 24 plus four is 28 plus nine is 37. So our final answer is 37

Angelo Rendina · Answer

we compute in a product between F and G and teases by definition given by the integral from 0 to 1 off fft times gft dirty So it&#x27;s just his integral. So these is the integral from 0 to 1 to now. I just developed the product so you can just completely yourself and f f t times GT becomes five t to the fourth power minus eight d cubed plus three t squared DT now just an issue of writing the primitive. So the premium of five t four is t to the fifth power. Then we have minus twice tete the fourth power. Then we have plus t cubed and this primitive is completed between zero and one. So it&#x27;s evaluated on one and then we subtract the primitive quality that zero and ah, you just replaced you with one and you get zero

Problem

Exercises $3-8$ refer to $\mathbb{P}_{2}$ with th…

Problem 6 Easy Difficulty

Exercises $3-8$ refer to $\mathbb{P}_{2}$ with the inner product given by evaluation at $-1,0,$ and $1 .$ (See Example $2 . )$
Compute $\|p\|$ and $\|q\|,$ for $p$ and $q$ in Exercise 4

Answer

$\sqrt{59}$

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

Linear Algebra and Its Applications

Lily A.

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Samuel H.

Michael J.

Vectors Intro

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$\sqrt{59}$

Linear Algebra and Its Applications

Lily A.

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Vectors Intro

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

Lily A.

Catherine R.

Samuel H.

Michael J.

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

Linear Algebra and Its Applications