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

Find a polynomial $p_{3}$ such that $\left\{p_{0}, p_{1}, p_{2}, p_{3}\right\}$ (see Exercise 11$)$ is an orthogonal basis for the subspace $\mathbb{P}_{3}$ of $\mathbb{P}_{4} .$ Scale the polynomial $p_{3}$ so that its vector of values is $(-1,2,0,-2,1)$

$\frac{5}{6} t^{3}-\frac{17}{6} t$

Calculus 3

Chapter 6

Orthogonality and Least Square

Section 7

Inner Product Spaces

Vectors

Campbell University

Oregon State University

University of Nottingham

Idaho State University

Lectures

02:56

In mathematics, a vector (…

06:36

03:46

Use this inner product to …

02:25

02:30

Let $S$ be the subspace of…

01:32

Find an orthogonal basis f…

Determine an orthonormal b…

03:49

Find an orthonormal basis …

04:32

05:53

Let $p_{1}(x)=1+x, p_{2}(x…

05:44

For Problems $15-18$, dete…

03:48

In Exercises 13 and 14, fi…

we have your focus now. Basis zero p one Batou, given by the polynomial is won T and T Square Minister. We know these from example Five. So I mean, let me right zero bar for the vector obtained by computing P zero in minus two. Imara swan in zero in one and into So this is just the vector off ones and then be one bar is minus two, minus 10 and two and finally P to bar. He's two minus one minus two minus one into. Now we write these vectors because we're called the dinner plucked between fully normals. So in this case, for instance, PCR against zero he's given by p zero bar don't p zero bar. Sonny's get is five, and similarly, we compute the one against the one to be 10 and p two against me, too, to be 14. We complete these numbers now because they're going to use them now. We'll soon when we're doing the Grand Street process. So let's go see there The Perimeter Cube, which is given by D Cubed. Let's right, Q bar, of course, is minus eight minus 101 and eight and we want to apply the garnish meat process to Q to obtain well obtain up vector riches or for colonel to both be zero p one MP too. So now the computation is simplified by the fact that the vectors p zero be wanting me to our world vectors. The polynomial sze p zero we won't be too are already or for Colonel. So all we need to do is to compute the projection off cue unwto p zero p one MP to Palestine would be zero, which is Q against zero divided by P 00 And of course, we recall that these is Q bar dot p zero bar divided by five the fire we computed previously and then P zeros of the constant function one and now you can compute a cube are 0.0 bars zero So this whole projection is the no vector. Then we compute the projection on Topi one off you seeming our lady this cure against the one divided by the one against the one you compute his number. It is the result to be 34 divided by 10 and then be wanted as the constant Well, the function t That's what these 3.4 t and finally the projection onto P to off you He's again Q against me, too divided by P two against me. To that multiplies the polynomial P too. And again you against see two turns out to be just zero. So this whole number is really bothered by 14. That multiplies the vector with very normal D squared minus two and he's just zero. And therefore we can put the three to make you minus all these projections. And the fourth is too cute miners, while the only thing they were subtracting 3.40. Finally, we're asked to scale this polynomial so that p three bar is minus 1202 and one. And of course, we see that in our particular case, be three bodies given my minus 1.220 months 2.4 and 1.2. So all we need to do is to scale this vector by one over 1.2, which is exactly 5/6. So if we divide by 1.2, we get the scale. Vector is carefully. Normal is 56 off a cube minus 17 6th off T. And in fact, this bully normal where we take the vector, Sit through it with the bar. He's exactly minus 1 to 0 minus two and one has wanted.

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…

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

Let $S$ be the subspace of $P_{3}(\mathbb{R})$ consisting of all polynomials…

Find an orthogonal basis for the span of the set $S$ in the vector space $V$…

Determine an orthonormal basis for the subspace of $\mathrm{C}^{3}$ spanned …

Find an orthonormal basis of the subspace spanned by the vectors in Exercise…

Let $p_{1}(x)=1+x, p_{2}(x)=-x+x^{2},$ and $p_{3}(x)=$ $1+2 x^{2} .$ Determi…

For Problems $15-18$, determine whether the given set $S$ of vectors is a ba…

In Exercises 13 and 14, find a basis for the subspace spanned by the given v…

01:55

Find the matrix of the quadratic form. Assume $\mathbf{x}$ is in $\mathbb{R}…

13:52

Find a QR factorization of the matrix in Exercise 11

04:15

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

01:12

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

03:01

Classify the quadratic forms in Exercises $9-18 .$ Then make a change of var…

04:27

Use only the definition of affine dependence to show that an indexed set $\l…

00:51

Compute the quantities in Exercises $1-8$ using the vectors$$\mathbf…

01:45

In Exercises $9-12,$ find (a) the orthogonal projection of $\mathbf{b}$ onto…

02:53

Find the singular values of the matrices.$\left[\begin{array}{ll}{3} &am…

00:30

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

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.