Let T and T2 two linear transformations from R? to R², defined by 7(;) - ) ()-() 3x - 2y (;) (; x+ y T2 y - 3x for all (x, y)" e R?. Find the standard matrix representations for each of the following composite functions, and their inverse transformation, if they exist, by using the algorithm for matrix inversion in Lemma 3, Topic 14. () T, followed by T2. (i) T2 followed by an anticlockwise rotation by angle 5 in R?. (ii) A reflection in the line y = 2x followed by a projection onto the line y = -3x in R2.
Let T and T2 two linear transformations from R? to R², defined by 7(;) - ) ()-() 3x - 2y (;) (; x+ y T2 y - 3x for all (x, y)" e R?. Find the standard matrix representations for each of the following composite functions, and their inverse transformation, if they exist, by using the algorithm for matrix inversion in Lemma 3, Topic 14. () T, followed by T2. (i) T2 followed by an anticlockwise rotation by angle 5 in R?. (ii) A reflection in the line y = 2x followed by a projection onto the line y = -3x in R2.
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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Transcribed Image Text:Let T and T2 two linear transformations from R? to R², defined by
7(;) - ) ()-()
3x - 2y
(;) (}
x+ y
T1
T2
y - 3x
for all (x, y)" e R?.
Find the standard matrix representations for each of the following composite functions, and their
inverse transformation, if they exist, by using the algorithm for matrix inversion in Lemma 3, Topic
14.
)T followed by T2.
(i) T2 followed by an anticlockwise rotation by angle 5 in R?.
(ii) A reflection in the line y = 2x followed by a projection onto the line y = -3x in R2.
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