💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

In Exercises 5 and $6,$ let $\mathbf{b}_{1}=\left[\begin{array}{l}{2} \\ {1} \\ {1}\end{array}\right], \mathbf{b}_{2}=\left[\begin{array}{r}{1} \\ {0} \\ {-2}\end{array}\right], \mathbf{b}_{3}=\left[\begin{array}{r}{2} \\ {-5} \\ {1}\end{array}\right]$ and $S=\left\{\mathbf{b}_{1}, \mathbf{b}_{2}, \mathbf{b}_{3}\right\} .$ Note that $S$ is an orthogonal basis for $\mathbb{R}^{3} .$ Write each of the given points as an affine combination of the points in the set $S,$ if possible.Hint: Use Theorem 5 in Section 6.2 instead of row reduction to find the weights.$$\text { a. }\mathbf{p}_{1}=\left[\begin{array}{r}{0} \\ {-19} \\ {-5}\end{array}\right] \quad \text { b. } \mathbf{p}_{2}=\left[\begin{array}{r}{1.5} \\ {-1.3} \\ {-.5}\end{array}\right] \text { c. } \mathbf{p}_{3}=\left[\begin{array}{r}{5} \\ {-4} \\ {0}\end{array}\right]$$

$p_{1}=-4 b_{1}+2 b_{2}+3 b_{3} \in$ affine $\mathrm{S}$$p_{2}=0.2 b_{1}+0.5 b_{2}+0.3 b_{3} \in$ affine $\mathrm{S}$$p_{3}=b_{1}+b_{2}+b_{3} \notin$ affine $\mathrm{S}$

Calculus 3

Chapter 8

The Geometry of Vector Spaces

Section 1

Affine Combinations

Vectors

Missouri State University

Oregon State University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

02:56

In mathematics, a vector (…

06:36

06:51

In Exercises 5 and $6,$ le…

03:39

In Exercises $1-6,$ determ…

03:27

01:58

02:44

01:21

02:43

03:15

In Exercises $3-6,$ verify…

03:44

In Exercises 1 and $2,$ yo…

Okay, So to solve this problem, we have that sings be one beat Sue B three are talking about busies are also gonna busies for all three. We can use the ends given so we can use serum five in section six. Points warned. So find the weeds C one seed su c three. So this implies that for P one for P won't we have that p one would be c one B one plus c two b two plus c three b three we're from If you look at that term five c want will be pee one more dots. Be one divided by B one dots Be one when you do this or on the name just right they see two quarts topi one dots productions be too over B two dots Beat Sue on, Then sit. There is a ghost O p one dot's big three overby three dots b three. Why do this? C one would just be When you don't for that's p one times, be one you have Ah zero minus 19 minus five. Does productive with sue on Juan divided by to woo Wan dogs Sue on one. You're gonna have minus 24 over six, which is minus four. If you do the same thing for C two, c two is P wand at zero minus night C minus five dots products, weeds beat Sue, which is 10 minus two. Divided by 10 minus tool under 10 minus TSU. You're gonna have 10 over five, which is a cost of sue. And then lastly off. See three, which is P one, which is zero minus and 19 minus five. Mort implied by Bizzarri, which is to minus five and one, then divided by Sue minus five on one. Soon minus five. Warn this will be night See over 30 which is a cost of three. So that implies I'm r p one is. I see one as minus four times be one plus two B two, blustery B three. So next. Wanna check if wanna check? If P one is in a fine of s so way added the coefficients, So scenes coefficient. Some p one is minors for plus two plus three, which is a ghost. +01 This implies that p one is fine off its send them. We do that for pizza. Ooh, So we said Pizza. Equal toe See one B one Plus it's to be too loss. It three beat everywhere. In this case, C one will be pizza because we're not dealing with pizza Monster played by be won over B one times does B one way. So for these, you're gonna have one point, Sue by six, which is zero point soon. Similarly sits who will be pizza? Ooh, dots beat So over beats two dots Beach Where does what we did for P one with? A lot of people are gonna have pizza, so this will be when you don't disagree. I have 2.5 over five, which is 0.5 and then last night. Sit there it is bead. Soon dots. Pizza does beat to be over beat Terry Dots Bizzarri, which is nine over 13 which is your 130.3. So this implies that's our pizza will be zero points to be won plus 0.5 beet soup plus 0.3 b three. So things the coefficients some the quick, efficient song off pizza is zero point Sue plus 0.5 blood 0.3, which is a ghost. Oh, Juan, This implies that he too easy off. Fine off s. Lastly, we do for teetering on, I would say beat the recall to see one B one plus seats will be two plus C three, Big three. We're in this case are. See, while we're not because you have Peter instead of Pete theory, don't be one over B one dot's bue on. You're gonna have six for six, which is one since you will be Jerry. Don't be too over beats with dots. Beat Sue. We're gonna have five over five. Does days on their last least Sitter is B three dots. Be very over Big three dots, Big Three. You're gonna off that sea over Fitz, which is just wrong. So, Thomas are Pete very equal to see? One is one. Not to be one close beats you. Close the three. Yeah, we see that. The coefficient some. The question, some off victory off victory is won. Lost one loss one, which is a cost of three. Which is not important. One. It's implies that Pete three is not I'm fine off this

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…

In Exercises 5 and $6,$ let $\mathbf{b}_{1}=\left[\begin{array}{l}{2} \\ {1}…

In Exercises $1-6,$ determine if the set of points is affinely dependent. (S…

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

In Exercises 1 and $2,$ you may assume that $\left\{\mathbf{u}_{1}, \ldots, …

04:37

Show that if an $n \times n$ matrix $A$ is positive definite, then there exi…

03:03

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

01:16

Find the maximum value of $Q(\mathbf{x})=7 x_{1}^{2}+3 x_{2}^{2}-2 x_{1} x_{…

02:55

In Exercises $3-6,$ find (a) the maximum value of $Q(x)$ subject to the cons…

01:04

Determine which pairs of vectors in Exercises $15-18$ are orthogonal.$$<…

02:45

In Exercises $21-24, \mathbf{a}, \mathbf{b},$ and $\mathbf{c}$ are noncollin…

04:29

Find an SVD of each matrix [Hint: In Exercise 11, one choice for $U$ is $\le…

15:04

A polyhedron $(3-\text { polytope) is called regular if all its facets }$ ar…

03:34

In Exercises 9 and $10,$ mark each statement True or False. Justify each ans…

04:19

Let$\mathbf{v}_{1}=\left[\begin{array}{r}{-1} \\ {-3} \\ {4}\end{array}\…

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.