Let f (z) = (az + b)/(cz + d) and ad bc + 0. If...

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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 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 +-).)