5. Give 2 x 2 matrices A so that for any x e R? we have, respectively: a. Ax is the vector whose components are, respectively, the sum and difference of the components of x. *b. Ax is the vector obtained by projecting x onto the line x1 = x2 in R?. c. Axis the vector obtained by first reflecting x across the line x1 = 0 and then reflecting the resulting vector across the line x2 = x1. d. Ax is the vector obtained by projecting x onto the line 2x1 – x2 = 0. *e. Ax is the vector obtained by first projecting x onto the line 2x1 – x2 = 0 and then rotating the resulting vector 7/2 counterclockwise. f. Ax is the vector obtained by first rotating x an angle of 1/2 counterclockwise and then projecting the resulting vector onto the line 2x1 – x2 = 0.

5. Give 2 x 2 matrices A so that for any x e R? we have, respectively: a. Ax is the vector whose components are, respectively, the sum and difference of the components of x. b. Ax is the vector obtained by projecting x onto the line x1 = x2 in R?. c. Axis the vector obtained by first reflecting x across the line x1 = 0 and then reflecting the resulting vector across the line x2 = x1. d. Ax is the vector obtained by projecting x onto the line 2x1 – x2 = 0. e. Ax is the vector obtained by first projecting x onto the line 2x1 – x2 = 0 and then rotating the resulting vector 7/2 counterclockwise. f. Ax is the vector obtained by first rotating x an angle of 1/2 counterclockwise and then projecting the resulting vector onto the line 2x1 – x2 = 0.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 7AEXP

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