3.4plz provide clear neat and handwritten answer for 3.4 3Let T : R? → R? be the linear transformation which reflects across the line y = -2x and then-3x-4y%3D-4x +3ystretches in the x and y directions, each by a factor of 5. That is, T3.1Verify, using what we've learned in class, that the formula given for T indeed performsthe transformation described geometrically above (reflecting across y = -2x and stretching by afactor of 5.)3.2Sketch 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.3.3Explain why your drawing from the previous part implies that neither e nor ez is aneigenvector for AT.3.4Determine two basic eigenvectors v1 and v2 for AT (you do not need to determine theeigenvalue(s) associated to those basic eigenvectors).Justify your answer using only a geometric explanation explicitly relying on and referring to yourdrawing from the previous part, or to a new drawing, if you wish.

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3.4 plz provide clear neat and handwritten answer for 3.4

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.1: Introduction To Linear Transformations

Problem 44E: For the linear transformation from Exercise 38, find a T(0,1,0,1,0), and b the preimage of (0,0,0),...

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Question

3.4

plz provide clear neat and handwritten answer for 3.4

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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