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Consider the following geometric 2 $\mathrm{D}$ transformations: $D,$ a Consider the following geometric 2 $\mathrm{D}$ transformations: $D,$ a dilation (in which $x$ -coordinates and $y$ -coordinates are scaleddilation (in which $x$ -coordinates and $y$ -coordinates are scaled

$R$ and $T$ do not commute. That is, $R T \neq T R$

Algebra

Chapter 2

Matrix Algebra

Section 7

Applications to Computer Graphics

Introduction to Matrices

Campbell University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

01:20

Consider the transformatio…

00:23

If $A^{\prime}, B^{\prime}…

00:31

Find the coordinates of th…

00:25

00:53

The points in the rectangu…

01:40

A figure has vertices at $…

00:33

The types of transformatio…

00:44

Determine the scale factor…

00:51

00:37

here We are not a dietitian, Dean, Cause Bye. Scaling the X coordinates and in white, coordinated by the same factor. So let's say we use facto arms. So if he's skilled the X coordinates off our 00 Your wife coordinates, you have zero are zero on, then this term is 01 So this is the dilation. Now we have our which is the rotation, which is giving us sign. If I sign off, I zero minus sign of five. Co sign off 50001 And then last week after seeing which is the translation, So recorded translation? Of course I did. Talk alone is that coordinates. Is that according to reserve 10 And then this is the transmission. That's the very reason each key and then we have one. So wanna check? Does our commutes who are sorry Does d committed Are so we calculates De Mort supplied by our when you multiply d by Are you have, um, cause sign off. I our sign off 50 my record at this hour. You can use any other Constance wants. Probably s O. C or whatever. I'm just it's an r so as minus our son Fei Our co sign of 50001 and then if you cockle it's our water supply by D, that is, Are they more displayed by D You're gonna have our co signed a fire out sign of 50 minus our sign of five are co signed a fire 000 So we have done scenes. Did our records are d It's implies that d on our commutes. Let's do the same thing for C on G. So let's see if c on dean are going to commute. So what we do is, um, did see if you multiply d bite See you off our 000 r zero are each are key on Don't want if your chocolates see more supply by Dean gonna off our 00 zero r zero age key. Why? So we see that scenes big seeing is not a quart to see g This implies off d on scene do nots commutes. So we have that. First of all, we are that are Andi commute now Dante does not commit lastly Wanna check if our and see commune so we calculate artsy artsy is actually your gets a call. Sign of five. Sign of 50 Minus sign of five. Course. Sign of 50 and gonna r H co sign off five minus key. Sign of five Each sign of five lost key course. Sign of five and go off on then. If you do this sentence, your computes see more to play by. Are you gonna have cause sign of five Sign of 50 minus sign of five. Course. Sign off. 50 on. Gonna have each key want. So we see that since R c is not the court to see our it implies that c are do nots commutes.

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