Find a single matrix for the transformation that is equivalent to doing the following four transformations of the plane in succession: 1. Shear by a factor of 7 in the x-direction. 2. Reflection over the line y = x. 3. Expand by a factor of 5 in the y-direction. 4. Rotate counter-clockwise by 90 degrees.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 17CM
icon
Related questions
Question
10/12 1a and 1b, Part of the same questions.
Find a single matrix for the transformation that is
equivalent to doing the following four transformations
of the plane in succession:
1. Shear by a factor of 7 in the x-direction.
2. Reflection over the line y = x.
3. Expand by a factor of 5 in the y-direction.
4. Rotate counter-clockwise by 90 degrees.
Check Answer
Transcribed Image Text:Find a single matrix for the transformation that is equivalent to doing the following four transformations of the plane in succession: 1. Shear by a factor of 7 in the x-direction. 2. Reflection over the line y = x. 3. Expand by a factor of 5 in the y-direction. 4. Rotate counter-clockwise by 90 degrees. Check Answer
Find the standard matrix for the linear transformation
T: R² → R² that shears vertically, with
1
1
T([J]) = [-3.7] ² and then reflects points about
the origin.
Check Answer
Transcribed Image Text:Find the standard matrix for the linear transformation T: R² → R² that shears vertically, with 1 1 T([J]) = [-3.7] ² and then reflects points about the origin. Check Answer
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage