Given the line L: and a linear transformation T:R R?. Let A denote the standard matrix of T and T(L) denote the image of the line L under the transformation T. a. Sketch the line L. 5. Sketch the line T(L) if A = - Describe the geometry of this trans- formation. e. Find a nonzero matrix A so that T(L) becomes a single point. 1. Find a matrix A so that T(2) becomes the line = +t 20 %3D 3 - Find a matrix A so that T(L) becomes the line 3 +t %3D E Find a matrix A so that T is a vertical shear and T(L) becomes a horizontal line. - Show that the line L can not be turned into a horizontal line using a hori- zontal shear.
Given the line L: and a linear transformation T:R R?. Let A denote the standard matrix of T and T(L) denote the image of the line L under the transformation T. a. Sketch the line L. 5. Sketch the line T(L) if A = - Describe the geometry of this trans- formation. e. Find a nonzero matrix A so that T(L) becomes a single point. 1. Find a matrix A so that T(2) becomes the line = +t 20 %3D 3 - Find a matrix A so that T(L) becomes the line 3 +t %3D E Find a matrix A so that T is a vertical shear and T(L) becomes a horizontal line. - Show that the line L can not be turned into a horizontal line using a hori- zontal shear.
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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Please solve only d,e,f,g parts
Transcribed Image Text:5. Given the line L
and a linear transformation
T:R? → R?.
Let A denote the standard matrix of T and T(L) denote the image of the line
Lunder the transformation T.
a. Sketch the line L.
b. Sketch the line T(L) if A =
Describe the geometry of this trans-
formation.
c. Find a nonzero matrix A so that T(L) becomes a single point.
20
d. Find a matrix A so that T(L) becomes the line|
%3D
e. Find a matrix A so that T(L) becomes the line
f. Find a matrix A so that T is a vertical shear and T(L) becomes a horizontal
line.
g. Show that the line L can not be turned into a horizontal line using a hori-
zontal shear.
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