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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
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linear algebra 2.2 Q5 

5. Give 2 x 2 matrices A so that for any x e R² 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 R². 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 rotating the resulting vector T /2 counterclockwise. f. Ax is the vector obtained by first rotating x an angle of n/2 counterclockwise and then projecting the resulting vector onto the line 2x1 – x2 = 0. - x2 = 0 and then
Transcribed Image Text:5. Give 2 x 2 matrices A so that for any x e R² 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 R². 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 rotating the resulting vector T /2 counterclockwise. f. Ax is the vector obtained by first rotating x an angle of n/2 counterclockwise and then projecting the resulting vector onto the line 2x1 – x2 = 0. - x2 = 0 and then
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