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
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,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0548f28d-2867-4ce8-91e2-809a65372be3%2Ffb4a26e9-75ac-4534-8374-b31917678d4c%2Fwpe1gya.png&w=3840&q=75)
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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