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

In Exercises 11 and $12,$ find the closest point to $y$ in the subspace $W$ spanned by $\mathbf{v}_{1}$ and $\mathbf{v}_{2} .$$$\mathbf{y}=\left[\begin{array}{l}{3} \\ {1} \\ {5} \\ {1}\end{array}\right], \mathbf{v}_{1}=\left[\begin{array}{r}{3} \\ {1} \\ {-1} \\ {1}\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{r}{1} \\ {-1} \\ {1} \\ {-1}\end{array}\right]$$

$\hat{y}=\left[\begin{array}{c}{3} \\ {-1} \\ {1} \\ {-1}\end{array}\right]$

Calculus 3

Chapter 6

Orthogonality and Least Square

Section 3

Orthogonal Projections

Vectors

Johns Hopkins University

Missouri State University

Campbell University

Oregon State University

Lectures

02:56

In mathematics, a vector (…

06:36

02:43

In Exercises 11 and $12,$ …

06:08

02:18

Let $\mathbf{y}, \mathbf{v…

02:12

04:56

In Exercises $7-10,$ let $…

03:43

03:13

In Exercises 1 and $2,$ yo…

04:06

Find the point on the plan…

03:48

In Exercises 13 and 14, fi…

so we want to find because this point toe why and the subspace w which is the span of the vectors of you want to be, too. So to do this, we know we need to find the orthogonal projection of why onto the span of you want to everyone a beat. So we have before meal for that. And that is why hat equals why dot b want over the one dot product with it. So Vanity one and some early with vegetable. So let's go ahead and find these dot products off to the side. So why not? Product would be one gives us three plus two minus one most 26. So we have 26 plus five is 31 minus one is 30 be one. That product with itself gives us one post for close one plus four, which gives us 10. So this first coefficient just 30 over 10 or three. So next, Uh, why dot product will be too. So we have minus 12. Find this one plus zero plus 39 so we get 39 minus 13 because it's 26 and gratitude out product with itself, you get 16 plus one plus zero, which gives us 26 as well. So second coefficient is just one. So now if we multiply these coefficients through three times 31 get three minus six minus 36 plus Ah, one times we too. So we just copy down too. And add these together. So three minus four. Negative one. Make it a five negative three and I So that's the vector that we won'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…

In Exercises 11 and $12,$ find the closest point to $y$ in the subspace $W$ …

In Exercises 11 and $12,$ find the dimension of the subspace spanned by the …

Let $\mathbf{y}, \mathbf{v}_{1},$ and $\mathbf{v}_{2}$ be as in Exercise $12…

In Exercises 11 and $12,$ give integers $p$ and $q$ such that Nul $A$ is a s…

In Exercises $7-10,$ let $W$ be the subspace spanned by the $\mathbf{u}^{\pr…

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

Find the point on the plane $4 x+3 y+z=2$ that is closest to the point $(1,-…

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

03:28

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

01:03

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

01:59

Determine which of the matrices in Exercises $7-12$ are orthogonal. If ortho…

07:43

Let $A$ be the matrix of the quadratic form$$9 x_{1}^{2}+7 x_{2}^{2}+11 …

03:58

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

04:07

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

04:18

In Exercises $7-12$ , use Example 6 to list the eigenvalues of $A$ . In each…

03:44

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

12:26

[MJ Use the method in this section to produce a QR factorization of the matr…

01:50

In Exercises 30 and $31,$ find the $\mathcal{B}$ -matrix for the transformat…

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.