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7. Consider the linear map f: R² R² determined by the following matrix cos(0)-sin(0) sin(0) cos(0) where 0 € R. (a) For which value of does / transform the line y into the line y = -x? (b) Give a geometric interpretation of the action of f on a vector (x, y). 8. Give a geometric interpretation of each the following transformations: (a) T(x,y)=(-1,-y). (b) S(x, y) = (x,-y).

7. Consider the linear map f: R² R² determined by the following matrix cos(0)-sin(0) sin(0) cos(0) where 0 € R. (a) For which value of does / transform the line y into the line y = -x? (b) Give a geometric interpretation of the action of f on a vector (x, y). 8. Give a geometric interpretation of each the following transformations: (a) T(x,y)=(-1,-y). (b) S(x, y) = (x,-y).

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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7. Consider the linear map f: R² R² determined by the following matrix (cos(0)-sin(0)) sin(0) cos(0) where 0 € IR. (a) For which value of 0 does f transform the line y = z into the line y = -x? (b) Give a geometric interpretation of the action of f on a vector (x, y). 8. Give a geometric interpretation of each the following transformations: (a) T(x, y) = (-x, -y). (b) S(x, y) = (x, y).
Transcribed Image Text:7. Consider the linear map f: R² R² determined by the following matrix (cos(0)-sin(0)) sin(0) cos(0) where 0 € IR. (a) For which value of 0 does f transform the line y = z into the line y = -x? (b) Give a geometric interpretation of the action of f on a vector (x, y). 8. Give a geometric interpretation of each the following transformations: (a) T(x, y) = (-x, -y). (b) S(x, y) = (x, y).
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