Let T : R? + R? be the linear transformation which reflects across the line y = -2x and then -3х — 4у -4x + 3y stretches in the x and y directions, each by a factor of 5. That is, T 3.1 Verify, using what we've learned in class, that the formula given for T indeed performs the transformation described geometrically above (reflecting across y = -2x and stretching by a factor of 5.) 3.2 Sketch a single copy of R? which contains the following: • T(e1) and T(e2), • The fundamental parallelogram for T (i.e. the image of the unit square under T), • The line y = -2x. 3.3 Explain why your drawing from the previous part implies that neither ej nor ez is an eigenvector for AT.
Let T : R? + R? be the linear transformation which reflects across the line y = -2x and then -3х — 4у -4x + 3y stretches in the x and y directions, each by a factor of 5. That is, T 3.1 Verify, using what we've learned in class, that the formula given for T indeed performs the transformation described geometrically above (reflecting across y = -2x and stretching by a factor of 5.) 3.2 Sketch a single copy of R? which contains the following: • T(e1) and T(e2), • The fundamental parallelogram for T (i.e. the image of the unit square under T), • The line y = -2x. 3.3 Explain why your drawing from the previous part implies that neither ej nor ez is an eigenvector for AT.
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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ques 3
plz provide answer for following parts of ques 3
Transcribed Image Text:3
Let T : R? → R? be the linear transformation which reflects across the line y = -2x and then
-3x-4y
%3D
-4x +3y
stretches in the x and y directions, each by a factor of 5. That is, T
3.1
Verify, using what we've learned in class, that the formula given for T indeed performs
the transformation described geometrically above (reflecting across y = -2x and stretching by a
factor of 5.)
3.2
Sketch a single copy of R2 which contains the following:
• T(e1) and T(e2),
• The fundamental parallelogram for T (i.e. the image of the unit square under T),
• The line y = -2x.
3.3
Explain why your drawing from the previous part implies that neither e nor ez is an
eigenvector for AT.
3.4
Determine two basic eigenvectors v1 and v2 for AT (you do not need to determine the
eigenvalue(s) associated to those basic eigenvectors).
Justify your answer using only a geometric explanation explicitly relying on and referring to your
drawing from the previous part, or to a new drawing, if you wish.
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