Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Let $p_{0}, p_{1},$ and $p_{2}$ be the orthogonal polynomials described in Example $5,$ where the inner product on $\mathbb{P}_{4}$ is given by evaluation at $-2,-1,0,1,$ and $2 .$ Find the orthogonal projection of $t^{3}$ onto $\operatorname{Span}\left\{p_{0}, p_{1}, p_{2}\right\}$

see answer

Calculus 3

Chapter 6

Orthogonality and Least Square

Section 7

Inner Product Spaces

Vectors

Missouri State University

Oregon State University

Baylor University

Boston College

Lectures

02:56

In mathematics, a vector (…

06:36

01:12

Exercises $3-8$ refer to $…

05:11

Let $V$ be the space $C[-2…

04:17

Find a polynomial $p_{3}$ …

17:52

Determine an orthogonal ma…

03:15

In Exercises $3-6,$ verify…

02:25

Use this inner product to …

03:58

Show that $\left\{\mathbf{…

06:12

D. Let $p(x)=2-x-x^{2}$ an…

03:46

03:44

Yes. Okay, so for this exercise, you got these three protectors point on. No. Uh, here. Okay, so this point on your speed, p zero b one b two are on B four. Okay. Aren't the evaluations, um, are defined as zero equals two minus two to one minus one 2 to 0 231 g four to. Okay, so these are the evaluations off the polynomial for that we're going to use to compute the inner product. And they remember that in this case, for arbitrary P and Q Yeah. Be cute. Elements off before the inner product is defined as a summation or from I equals to zero toe four or be evaluated. A the I times. Cute. Evaluated a t. I. Okay, so this is the way off. How? It's fine here. The inner product that is off. Okay. Onto the space. Okay, So let us define so left. Consider, love you of the spun off zero. Be one YouTube. Okay, on. We're going to consider affect. Cute. Given by the cute on. We need to compute the production off. Cute on the subspace office on the space pine by p zero p one and p two. So this is a So this projection eyes define us the in their product off cube, with zero divided by the inner product off easier with itself. Times zero love to with the one you same claims to be one on the other victors. Pete too. Okay, so let us start competing these values here, these in their problems. So the inner product you think mhm Cuban zero is equal to to taking the inner product off the cube one. Okay, the values off the teeth are zero equals minus three minus one 2 to 0. It's right here in three years to t three is one on T four is equal Stoute. So this in the product is going to be minus two. Que waas minus one cube. Last one, cube glass to cube. And this is just zero. Okay, so this term is not going to to a port, Anything to this projection. So this value just here. Let's continue with this one. Things. Problems between Q on p one is just taking Thank you team on this When we're going to evaluate, it is minus two to the fourth plus minus +14 plus +14 lost to the fore. This is just 34. And then let's compute this inner product here. So cute on beat. So get this three. Cool square. Okay, minus two. Do you square minus two. And this is minus two to the three. Four minus two plus minus three minus one. Cooper one minus two plus one. Cute one plus one minus two. Um, blast to cube four minus two. Okay, so here this term council, with this term on this term council with this one. So this is just zero. So these other term also becomes zero. So we just need to focus on this time here. We have already compute this one. So we need to compute the inner product off the one with itself. So the inner product off the one with itself, he just taking the inner product off the with cheap. And this is minus two square plus minus one square, plus one squared. Plus two square on. This is supposed to tell. Okay, so at the end, the protection off the vector cute on the view. Is it close to 34 divided 10 t

View More Answers From This Book

Find Another Textbook

In mathematics, a vector (from the Latin word "vehere" meaning &qu…

In mathematics, a vector (from the Latin "mover") is a geometric o…

Exercises $3-8$ refer to $\mathbb{P}_{2}$ with the inner product given by ev…

Let $V$ be the space $C[-2,2]$ with the inner product of Example $7 .$ Find …

Find a polynomial $p_{3}$ such that $\left\{p_{0}, p_{1}, p_{2}, p_{3}\right…

Determine an orthogonal matrix $S$ such that $S^{T} A S=\operatorname{diag}\…

In Exercises $3-6,$ verify that $\left\{\mathbf{u}_{1}, \mathbf{u}_{2}\right…

Use this inner product to determine an orthogonal basis for the subspace of …

Show that $\left\{\mathbf{u}_{1}, \mathbf{u}_{2}\right\}$ or $\left\{\mathbf…

D. Let $p(x)=2-x-x^{2}$ and $q(x)=1+x+x^{2} .$ Using the inner product$$…

11:17

In Exercises $1-4,$ find a least-squares solution of $A \mathbf{x}=\mathbf{b…

08:40

Let $p_{0}, p_{1},$ and $p_{2}$ be the orthogonal polynomials described in E…

02:48

Find the characteristic polynomial and the eigenvalues of the matrices in Ex…

04:24

Exercises $21-24$ refer to $V=C[0,1],$ with the inner product given by an in…

04:14

Involve a design matrix $X$ with two or more columns and a least-squares sol…

03:22

Find the equation $y=\beta_{0}+\beta_{1} x$ of the least-squares line that b…

01:03

06:55

Given $a \geq 0$ and $b \geq 0,$ let $\mathbf{u}=\left[\begin{array}{c}{\sqr…

03:28

Use the inner product axioms and other results of this section to verify the…

06:30

Chapter 7 will focus on matrices $A$ with the property that $A^{T}=A$ . Exer…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.