Let (1,2) be a point of R2. Let R be the rotation through an angle of /4. What are thecoordinates of R(1,2) relative to the usual basis {(1,0), (0, 1)}.PROBLEM 2.2.3 Let R be a rotation through an angle 0. Show that for any vector v = (x, y) inR² we have ||v|| = ||R(v)||, where ||(x,y)|| = √√x² + y².PROBLEM 2.2.4 Let c be a real number, and let f: R³ R³ be the linear map such thatf(v) = cv, where v R³. What is the matrix associated with this linear map?

As per the guidelines I am answering only one question Remember Rotation matrix by an angle θ is…

Answered: Let (1,2) be a point of R². Let R be…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find the coordinates of x = {-10, 2, 4} with respect to the basis consisting of u, {1, 3, 2}, u, = {2, 1, 4}, and u; = {1,0, 6}. -
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Let (1,2) be a point of R². Let R be the rotation through an angle of 1/4. What are the coordinates of R(1,2) relative to the usual basis {(1,0), (0, 1)}.