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3) For each transformation, find the 2 x 2 matrix that corresponds to T by finding the images of (1,0) and (0,1). Find the determinant of T. e) Projection: given a fixed vector line spanned by 7 (a, b), T maps each point to the closest point on the F12 a2 ab a2+b2 a2 b2 = 0 Answer in book: det b2 ab a2+b2 12+b2 f) Reflection: given a fixed vector 7 = (a, b), T maps each point to its reflection with respect to r T(x - 2x, = 2x, - F 'a2-b2 2ab a2+b2 a2+b2 -1 Answer in book: det b2-а? 2ab a2+b2 a2+b2

3) For each transformation, find the 2 x 2 matrix that corresponds to T by finding the images of (1,0) and (0,1). Find the determinant of T. e) Projection: given a fixed vector line spanned by 7 (a, b), T maps each point to the closest point on the F12 a2 ab a2+b2 a2 b2 = 0 Answer in book: det b2 ab a2+b2 12+b2 f) Reflection: given a fixed vector 7 = (a, b), T maps each point to its reflection with respect to r T(x - 2x, = 2x, - F 'a2-b2 2ab a2+b2 a2+b2 -1 Answer in book: det b2-а? 2ab a2+b2 a2+b2

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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How did they get these answeres for e and f. I have listed answers with questions but dont know how they got them

3) For each transformation, find the 2 x 2 matrix that corresponds to T by finding the images of (1,0) and (0,1). Find the determinant of T. e) Projection: given a fixed vector line spanned by 7 (a, b), T maps each point to the closest point on the F12 a2 ab a2+b2 a2 b2 = 0 Answer in book: det b2 ab a2+b2 12+b2 f) Reflection: given a fixed vector 7 = (a, b), T maps each point to its reflection with respect to r T(x - 2x, = 2x, - F 'a2-b2 2ab a2+b2 a2+b2 -1 Answer in book: det b2-а? 2ab a2+b2 a2+b2
Transcribed Image Text:3) For each transformation, find the 2 x 2 matrix that corresponds to T by finding the images of (1,0) and (0,1). Find the determinant of T. e) Projection: given a fixed vector line spanned by 7 (a, b), T maps each point to the closest point on the F12 a2 ab a2+b2 a2 b2 = 0 Answer in book: det b2 ab a2+b2 12+b2 f) Reflection: given a fixed vector 7 = (a, b), T maps each point to its reflection with respect to r T(x - 2x, = 2x, - F 'a2-b2 2ab a2+b2 a2+b2 -1 Answer in book: det b2-а? 2ab a2+b2 a2+b2
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