(2) (8 points) Find the linear fractional transformation w = T(-) that maps points {0, 1,...
(c) please Tz that 1. Find the most general linear fractional transformation w = maps the region A into B : (a) A = {l-1 <1}, B = {Im w >0} (6) A = {lz| <1}, B= {Rew >0} (c) A = {]z – al < R}, B = {Rew 5-3}
Problem 2. (18 points) (a) Find a fractional linear transformation that maps the right half-plane to the unit disk such that the origin is mapped to -1. (b) A fixed point of a transformation T is one where T(2) = 2. Let T be a fractional linear transformation. Assume T is not the identity map. Show T has a most two fixed points. (c) Let S be a circle and 21 a point not on the circle. Show that there...
z+1 The linear fractional transformation shown below is related to w = u + jv and z = x + jy w= z-2' a. Calculate the curves that the lines v = constant maps to in the x-y plane, b. Calculate the curves that the lines y = constant maps to in the u-v plane, c. What is the line in the x-y plane that maps to a line in the u-v plane?
7. Consider the fractional linear transformation that maps -1 to -2i, 1 to i and i to 0. Determine the image of the unit circle EC 1 the image of the open unit disk (z EC<1), and the image of the interval [-1,1 on the real axis Illustrate with a sketch
Find the matrix [T], p of the linear transformation T: V - W with respect to the bases B and C of V and W, respectively. T:P, → P, defined by T(a + bx) = b - ax, B = {1 + x, 1 – x}, C = {1, x}, v = p(x) = 4 + 2x [T] C+B = Verify the theorem below for the vector v by computing T(v) directly and using the theorem. Let V and W...
1. Let T(2) := tbe a fractional linear transformation, as above (so a, b, c, d e C with ad-bc7 0). Argue that T is differentiable everywhere except one point and find T'(2). (Don't prove it directly - use results from class.) When is T' (2) = 0? What happens if the condition on coefficients is not met, i.e. if ad-bc=0? What can you say about the function in this case?
Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 37 1 -2 A=-1 3 -4 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R O One-to-one; onto R O Not one-to-one: onto O Not one-to-one; not onto OOne-to-one: not onto
Find the matrix of the linear transformation T: V →W relative to B and C. Suppose B = {bı, b2, b3} is a basis for V and C = {C1, C2} is a basis for W. Let T be defined by T(b]) = 261 + C2 T(62) = -501 +502 T(b3) = 2C1-802 2. 3 0 2 -6 [3 0 -6 1 5-8 2 -5 2 5 -8 2 1 -5 5 2 -8
(a) Find a Möbius transformation that maps 0 to, 1 to 2, and -1 to 4 (b) Let h(z)be the Möbius transformation and C: z-21 2 be the circle 2z-8 with centre 2 and radius 2. Determine the image of the interior of the circle C under h(z). (a) Find a Möbius transformation that maps 0 to, 1 to 2, and -1 to 4 (b) Let h(z)be the Möbius transformation and C: z-21 2 be the circle 2z-8 with centre...
Example 3: Find the bilinear transformation that maps the points (o, i, 0) into the points JNTU 2003 (Set No. I)I 0, i, 0o)