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).

Answered: Image /qna-images/answer/ae6e8097-721e-4ade-8e6a-ae87142ffbc0.jpg

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).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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Similar questions

Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
For the linear transformation from Exercise 45, let =45 and find the preimage of v=(1,1). 45. Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a T(4,4) for =45, b T(4,4) for =30, and c T(5,0) for =120.

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