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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)}.

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)}.

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
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Let (1,2) be a point of R2. Let R be the rotation through an angle of /4. What are the coordinates 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) in R² 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 that f(v) = cv, where v R³. What is the matrix associated with this linear map?
Transcribed Image Text:Let (1,2) be a point of R2. Let R be the rotation through an angle of /4. What are the coordinates 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) in R² 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 that f(v) = cv, where v R³. What is the matrix associated with this linear map?
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