Let f(z) = (az + b)/(cz + d) and ad – bc # 0. If this transformation maps zo → Wo, 1→ W1 and Z2 → W2 (in other words, if three points and their images under this bi-linear cransformation is specified) show that f(z) can be found uniquely. (Hint: Write Wi = (az; + b)/(cz; + d), i = 0,1,2 and convert this three equation to a linear equation system of three equations, whose unknown b c c are,, and the right hand side includes terms having zo, Z1, Z2, Wo, W1, W2. Then, solve ,, b d
Let f(z) = (az + b)/(cz + d) and ad – bc # 0. If this transformation maps zo → Wo, 1→ W1 and Z2 → W2 (in other words, if three points and their images under this bi-linear cransformation is specified) show that f(z) can be found uniquely. (Hint: Write Wi = (az; + b)/(cz; + d), i = 0,1,2 and convert this three equation to a linear equation system of three equations, whose unknown b c c are,, and the right hand side includes terms having zo, Z1, Z2, Wo, W1, W2. Then, solve ,, b d
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 48E: For the linear transformation T:R2R2 given by A=[abba] find a and b such that T(12,5)=(13,0).
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Question
Let f (z) = (az + b)/(cz + d) and ad – bc + 0. If this transformation maps zo Wo, Z1 → W1 and z2 → W2 (in other words, if three points and their images under this bi-linear transformation is specified) show that f (z) can be found uniquely. (Hint: Write W; = (az; + b)/(cz; + d), i = 0,1,2 and convert this three equation to a linear equation system of three equations, whose unknowns b c d are and the right hand side includes terms having z0, Z1, Z2, Wo, W1, W2. Then, solve b c d in а а' а a'a'a b. d. terms of zo, Z1, Z2, Wo, W1, W2 and find f(z) = (z +)/Ez +-).)
![Let f(z) = (az + b)/(cz + d) and ad – bc + 0. If this transformation maps zo → Wo,
Z1 → W1 and z2 → W2 (in other words, if three points and their images under this bi-linear
transformation is specified) show that f (z) can be found uniquely. (Hint: Write
W; = (az; + b)/(cz; + d), i = 0,1,2
and convert this three equation to a linear equation system of three equations, whose unknowns
b c d
are
and the right hand side includes terms having Zo, Z1, Z2, Wo, W1, W2. Then, solve
b c d
in
а а' а
а а' а
b.
d.
terms of Zo, Z1, Z2, Wo, W1, W2 and find f(z) = (z +)/Ez +).)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f4f4054-ff6a-4a4a-ada4-6767e562d0a5%2F98b57c41-580b-4634-9b0a-eb0a25e41fa6%2Foap7ce8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let f(z) = (az + b)/(cz + d) and ad – bc + 0. If this transformation maps zo → Wo,
Z1 → W1 and z2 → W2 (in other words, if three points and their images under this bi-linear
transformation is specified) show that f (z) can be found uniquely. (Hint: Write
W; = (az; + b)/(cz; + d), i = 0,1,2
and convert this three equation to a linear equation system of three equations, whose unknowns
b c d
are
and the right hand side includes terms having Zo, Z1, Z2, Wo, W1, W2. Then, solve
b c d
in
а а' а
а а' а
b.
d.
terms of Zo, Z1, Z2, Wo, W1, W2 and find f(z) = (z +)/Ez +).)
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