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 15 and $16,$ use the factorization $A=Q R$ to find the least-squares solution of $A \mathbf{x}=\mathbf{b} .$$$A=\left[\begin{array}{ll}{2} & {3} \\ {2} & {4} \\ {1} & {1}\end{array}\right]=\left[\begin{array}{rr}{2 / 3} & {-1 / 3} \\ {2 / 3} & {2 / 3} \\ {1 / 3} & {-2 / 3}\end{array}\right]\left[\begin{array}{rr}{3} & {5} \\ {0} & {1}\end{array}\right], \mathbf{b}=\left[\begin{array}{l}{7} \\ {3} \\ {1}\end{array}\right]$$

$\hat{x}\left[\begin{array}{c}{4} \\ {-1}\end{array}\right]$

Calculus 3

Chapter 6

Orthogonality and Least Square

Section 5

Least-Squares Problems

Vectors

Oregon State University

Harvey Mudd College

Baylor University

University of Nottingham

Lectures

02:56

In mathematics, a vector (…

06:36

01:17

In Exercises 15 and $16,$ …

11:17

In Exercises $1-4,$ find a…

02:18

02:05

01:57

In Exercises $1-16,$ an eq…

02:13

An equation is given, foll…

00:41

In Exercises $1-64$, solve…

01:15

00:35

00:50

we are given the cue are the composition of a I want to find the least choir solution to a X equal Be so we first started computing que transposed being you do the multiplication and turns out to be 17 house and nine hours. And now since we have the cure the composition, we can find the least square solution By solving the system, Our ex hat is equal to you. Transpose be now our ease up square two by two metrics So we can just all way by inverting are so x hot is equal to well, the inverse of our turns out to be 1/10 off five months 302 That multiplies u transpose being so 17 house and nine house So 1/10 off we do the multiplication So we're left with 29 9 So the solution for X hat he's the vector 2.90 point nine And this is the least square solutions

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 15 and $16,$ use the factorization $A=Q R$ to find the least-sq…

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

In Exercises $1-16,$ an equation is given, followed by one or more roots of …

An equation is given, followed by one or more roots of the equation. In each…

In Exercises $1-64$, solve each of the given equations. If the equation is q…

01:04

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

02:53

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

07:11

Find an orthogonal basis for the column space of each matrix in Exercises $9…

02:45

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

01:41

Verify the statements in Exercises $19-24 .$ The matrices are square.If …

00:53

Find the singular values of the matrices.$\left[\begin{array}{rr}{1} &am…

02:25

Suppose radioactive substances $\mathrm{A}$ and $\mathrm{B}$ have decay cons…

07:49

In Exercises 25 and $26,$ mark each statement True or False. Justify each an…

05:22

Exercises $9-14$ require techniques from Section $3.1 .$ Find the characteri…

04:41

The space is $C[0,2 \pi]$ with the inner product $(6)$.Show that $\sin m…

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.