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Show that the transformation in Exercise 8 is merely a rotation about the origin. What is the angle of the rotation?

The angle of rotation is $\frac{\pi}{2}$ or 90 deg.

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 9

The Matrix of a Linear Transformation

Introduction to Matrices

McMaster University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

00:36

Find the degree measure of…

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04:13

Show that the transformati…

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Find the radian measure of…

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Find a new representation …

00:31

Determine the coordinates …

So we want to use the transformation from exercise east. And so we have this, uh, matrix t just the standard metrics. So we know that the first call in is t of anyone, and the second call is t of each ago. Maybe we should call this something different. Well, call it a so we wouldn't show that this is just a rotation about the origin. And we want to find out how many degrees directors are being rotated. So we know the one iss vector 10 And he, too, was the vector zero. So let's go ahead and plot the map ings. So we want is 10 So that is this rector here, and we know that after reply the transformation t t of the one is 01 because that's the first column. So is he wrote one hiss inspector here so we can see that our original vector the one is rotated, uh, counterclockwise, 90 degrees. So let's do the same thing with me too. So you two whoops is the factor. 10 We're sorry. 01 Which is the specter here? And TV, too? It's the second column, which is negative 10 which is this factor here. So I can see again. As in the first case, our director is rotated to the left about the origin 90 degrees. So we have a, uh our degree of rotation ISS to the left. So it's negative. We can say negative 90 degrees or negative pi over to radiance.

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