assig7_2011 - after transforming it by a linear...

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Math 152, Spring 2011 Assignment #7 Notes: Each question is worth 5 marks. Due in class: Monday, February 28 for MWF sections; Tuesday, March 1 for TTh sections. Solutions will be posted Tuesday, March 1 in the afternoon. No late assignments will be accepted. 1. Find the matrix of each of the following linear transformations: (a) L ( x,y,z ) = (2 x - 3 y + z, 4 y - 2 z,x + 2 z ) . (b) L : R 2 R 2 . First rotate by 45 counterclockwise, then reﬂect in the y -axis and ﬁnally project to the line x = y . 2. Find a 2 × 2 matrix A 6 = I , such that A 3 = I . (Hint: think about linear transformations.) 3. Let v = [3 , 2]. Find the rotation of v by the angle 60 counterclockwise. 4. Consider the matrices A = ± 1 1 0 1 ² , B = ± 0 1 - 1 0 ² . Notice that B is a rotation matrix. Let S = { (0 ,y ) | 0 y 1 } be the line segment on the y -axis. (a) Draw the images of the point (0 , 1) after transforming it by matri- ces A,B,AB and BA . (You should get 4 points in R 2 .) (b) Draw the images of the line segment S after transforming it by matrices A,B,AB and BA. (The image of S

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Unformatted text preview: after transforming it by a linear transformation L is { L ( s ) | all s in S } . (c) Describe in words how you could use MATLAB to verify your results in (a). Enter matlab plot into google to read about the plot command that should help you determine what to do. 5. Let R : R 2 R 2 be the rotation by angle counterclockwise. Let F : R 2 R 2 be the reection in the line that makes angle with the positive x-axis. The composition of any two of these linear trans-formations is again a rotation or a reection. In each case below, nd which one it is, and what is the angle. (For example, R R = R + . You dont need matrices to solve this problem. Draw the images of the vectors e 1 and e 2 by the compositions and nd which rotation or reection has these images.) (a) R F . (b) F F ....
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This note was uploaded on 03/30/2011 for the course MATH 152 taught by Professor Caddmen during the Spring '08 term at The University of British Columbia.

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assig7_2011 - after transforming it by a linear...

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