College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 6 - Summary, Review, and Test - Review Exercises - Page 657: 35

Answer

Rotation by $90$ degrees counterclockwise

Work Step by Step

The matrix of the initial triangle's coordinates is: $B=\begin{bmatrix}0&2&2\\0&0&-4\end{bmatrix}$ Consider matrix $A$: $A=\begin{bmatrix}0&-1\\1&0\end{bmatrix}$ Compute $AB$: $AB=\begin{bmatrix}0&-1\\1&0\end{bmatrix}\begin{bmatrix}0&2&2\\0&0&-4\end{bmatrix}$ $=\begin{bmatrix}0+0&0+0&0+4\\0+0&2+0&2+0\end{bmatrix}$ $=\begin{bmatrix}0&0&4\\0&2&2\end{bmatrix}$ We notice that the new triangle is the initial triangle rotated by $90$ degrees counterclockwise.
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