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Show that the transformation in Exercise 7 is equivalent to a rotation about the origin followed by a translation by $\mathbf{p}$ . Find $\mathbf{p} .$

$p=\left[\begin{array}{l}{3+4 \sqrt{3}} \\ {4-3 \sqrt{3}}\end{array}\right]$

Algebra

Chapter 2

Matrix Algebra

Section 7

Applications to Computer Graphics

Introduction to Matrices

Missouri State University

McMaster University

Lectures

01:32

In mathematics, the absolu…

01:11

02:34

Show that the transformati…

02:50

Given: $\overline{A^{\prim…

00:38

Suppose you reflected this…

03:04

Determine the coordinates …

01:21

In Exercises $57-61$ , pro…

03:34

Using the point $P(x, y)$ …

02:44

Let $T : \mathbb{R}^{m} \r…

03:25

04:28

01:40

No. From exercise seven Exercise seven. The transformation metrics waas um, one of its su words. Three over to sue zero minus with three over the zoo off zero three plus four words three four minus three with three un, then warm. Now observe that we can rides. We can write this matrix in the form a zero transpose p unworn. We're in this case will be this metrics which is one over to Sue Woods theory over the zoo. My nursery story over. Zoo one over. Too soon on them p will be this two by one Matrix wolf three loss for words three I'm four minus three birds three No. Um bye. Exercise that scene. This many trees a zero transpose p Juan Come Bharat Singh. As I zero transpose he is a p warm. A 00 transports on dhe warn Now what this tells us is this which is just the composition off a linear transformation in our sue on dhe. A translation. So the translation is the pea mitri. Is that so? The translation is days is the pee on then the linear transformation is the A and I'm gonna explain It's now No, the MICEX, eh? Is the Matrix over a petition about the origin? We can see that about the origin in art Sue thaws the transformation in exercise seven is the composition off. So it set off a compression within their transformation. The linear transformation is a matrix of rotation. So is a composition off the rotation about urging on dhe translation by P. So we're just much in this for these on then. The translation is given by people.

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