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2) Which of the following are linear transformations from R2 - R2? (a) Shear: T(x, y) (x + cy,y) for some constantc T T()T() -C] T(cu) cT (u) u = (b) Translation: T(x, y) = (x + a, y + b) for some constants a and b (c) Blow-up: T(x, y) (ax, by) for some constants a and b (d) Rotation: if x = rcos0, y = rsin0, then T(x, y) (rcos(0 p), rsin(0 p)) for some constants angle p (e) Projection: given a fixed vector r = (a, b), T maps each point to the closest point on the line spanned by T |712 (f) Reflection: given a fixed vector r = (a, b), T maps each point to its reflection with respect to r 2x T ( = 2x,

2) Which of the following are linear transformations from R2 - R2? (a) Shear: T(x, y) (x + cy,y) for some constantc T T()T() -C] T(cu) cT (u) u = (b) Translation: T(x, y) = (x + a, y + b) for some constants a and b (c) Blow-up: T(x, y) (ax, by) for some constants a and b (d) Rotation: if x = rcos0, y = rsin0, then T(x, y) (rcos(0 p), rsin(0 p)) for some constants angle p (e) Projection: given a fixed vector r = (a, b), T maps each point to the closest point on the line spanned by T |712 (f) Reflection: given a fixed vector r = (a, b), T maps each point to its reflection with respect to r 2x T ( = 2x,

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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2) Which of the following are linear transformations from R2 - R2? (a) Shear: T(x, y) (x + cy,y) for some constantc T T()T() -C] T(cu) cT (u) u = (b) Translation: T(x, y) = (x + a, y + b) for some constants a and b (c) Blow-up: T(x, y) (ax, by) for some constants a and b (d) Rotation: if x = rcos0, y = rsin0, then T(x, y) (rcos(0 p), rsin(0 p)) for some constants angle p (e) Projection: given a fixed vector r = (a, b), T maps each point to the closest point on the line spanned by T |712 (f) Reflection: given a fixed vector r = (a, b), T maps each point to its reflection with respect to r 2x T ( = 2x,
Transcribed Image Text:2) Which of the following are linear transformations from R2 - R2? (a) Shear: T(x, y) (x + cy,y) for some constantc T T()T() -C] T(cu) cT (u) u = (b) Translation: T(x, y) = (x + a, y + b) for some constants a and b (c) Blow-up: T(x, y) (ax, by) for some constants a and b (d) Rotation: if x = rcos0, y = rsin0, then T(x, y) (rcos(0 p), rsin(0 p)) for some constants angle p (e) Projection: given a fixed vector r = (a, b), T maps each point to the closest point on the line spanned by T |712 (f) Reflection: given a fixed vector r = (a, b), T maps each point to its reflection with respect to r 2x T ( = 2x,
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