Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Are the two linear transformations the same? Yes S: R² R2, shear such that √3 4 B 2 maps to OB 1 4 1 √3 and then scale vertically by a factor of followed by shear such that • T: R² → R², rotate counterclockwise 150° about the origin, scale horizontally by a factor of √3 2 [] 2 733 √√√3 maps to

Are the two linear transformations the same? Yes S: R² R2, shear such that √3 4 B 2 maps to OB 1 4 1 √3 and then scale vertically by a factor of followed by shear such that • T: R² → R², rotate counterclockwise 150° about the origin, scale horizontally by a factor of √3 2 [] 2 733 √√√3 maps to

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

Explain how to answer this question:

Are the two linear transformations the same? Yes ✅ - **S: ℝ² → ℝ²**, shear such that \(\begin{bmatrix} 1 \\ 0 \end{bmatrix}\) maps to \(\begin{bmatrix} 1 \\ -\frac{1}{\sqrt{3}} \end{bmatrix}\) followed by shear such that \(\begin{bmatrix} 0 \\ 1 \end{bmatrix}\) maps to \(\begin{bmatrix} \frac{\sqrt{3}}{4} \\ 1 \end{bmatrix}\). - **T: ℝ² → ℝ²**, rotate counterclockwise 150° about the origin, scale horizontally by a factor of \(-\frac{\sqrt{3}}{2}\), and then scale vertically by a factor of \(-\frac{2}{\sqrt{3}}\).
Transcribed Image Text:Are the two linear transformations the same? Yes ✅ - **S: ℝ² → ℝ²**, shear such that \(\begin{bmatrix} 1 \\ 0 \end{bmatrix}\) maps to \(\begin{bmatrix} 1 \\ -\frac{1}{\sqrt{3}} \end{bmatrix}\) followed by shear such that \(\begin{bmatrix} 0 \\ 1 \end{bmatrix}\) maps to \(\begin{bmatrix} \frac{\sqrt{3}}{4} \\ 1 \end{bmatrix}\). - **T: ℝ² → ℝ²**, rotate counterclockwise 150° about the origin, scale horizontally by a factor of \(-\frac{\sqrt{3}}{2}\), and then scale vertically by a factor of \(-\frac{2}{\sqrt{3}}\).
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS