Determine the Mobius transformation mapping 0 to 2, 2i to 0 and i to 3/2
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3 2 0 3. Compute the product 0 01-1 0 013 4. If the matrix A from the previous problem represents a linear transformation T, determine: (a.) Is the mapping onto (b.) Is the mapping one to one (c.) Is the mapping homomorphic (d.) Is the mapping isomorphic (e.) What is the range space? The rank? (f) What is the null space? The nullity? (g.) Does this transformation preserve magnitude? 5. (a.) What is AT, the transpose of the matrix...
2. Determine whether or not the mapping f: R+R given by f(0) = 2 is a transformation. 3. Determine whether or not the mapping f: RR given by f(2)= is a transformation. 4. Determine whether or not the mapping f:R2 + R2 given by far,y) = (2x, 3y) is a transformation.
9. For each of the following, provide a suitable example, or else explain why no such example exists. [2 marks each]. a) A function f : C+C that is differentiable only on the line y = x. b) A function f :C+C that is analytic only on the line y = x. c) A non-constant, bounded, analytic function f with domain A = {z | Re(z) > 0} (i.e., the right half-plane). d) A Möbius transformation mapping the real axis...
Here is an example of how to do it. 5. Let t be the inversive transformation defined by Determine the image of each of the following generalized circles under : (a) the extended line E U foo], where E is the line with equation y-x (b) the unit circle . 310 5: Inversive Geometry Problem 7 Let be the inversive transformation defined by 2-2i r(z) = 2. 2+2 Use the strategy to determine the image of each of the following...
10. Mobius transformations. Let a, b, c, d ad-bc 0 . The function is called a Mobius transformation (or linear fractional transformation). Show that a) lim z->inf T(z) = inf if c=0; b)kim z-> inf T(z) = a/c and lim z-> d/c T(z) = inf if c0 *10. Möbius transformations. Let a,b,c,d EC with ad-bc70. The function T(2) = 2 a2 + b cz + d à (2 +-d/c) is called a Möbius transformation (or linear fractional transformation). Show that...
Help with detail answer. Consider the following: w g(z)where w is the fractional linear (Mobius) transformation Describe and sketch the image set of g(B) if B is the annulus { z ε ¢ : 1 < Izi < 2} Consider the following: w g(z)where w is the fractional linear (Mobius) transformation Describe and sketch the image set of g(B) if B is the annulus { z ε ¢ : 1
two seperate questions multiple choice Calculate the following: [3+i 2-i [ [ 3 2 2-i| 2 ས 3 2- 2i - 3 2- 2i 2 - 1 Determine the real and imaginary parts of the complex number by first writing the number in standard form. z=(5-3i)(5 + 3i) Re(z) = 30 and Im(z) = 4 Re(z) = 32 and Im(z) = 2 Re(z) = 34 and Im(z) = 6 Re(z) = 34 and Im(z) = 0
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
Consider the molecule BrF5 shown whose structure is shown below (the four fluorine atoms forming a plane make a square). 3) Consider the molecule BrF5 shown whose structure is shown below (the four fluorine atoms forming a plane make a square) [18 marks] 168.9 pm84.8 Fi, 77.4 pm [Wikipedia e] i) what is the point group for this molecule? ii) draw the symmetry elements contained in the molecule iii) derive the 2x2 transformation matrix (mapping matrix) for the x and...
2. Let b(1,-1,1). Define T: R3R3 by the mapping: T(x) (x b)b (a) Show that T is a linear transformation by verifying the two linear transformation axioms (b) Determine the standard matrix representation for T. (c) Give a geometrical interpretation of T. 2. Let b(1,-1,1). Define T: R3R3 by the mapping: T(x) (x b)b (a) Show that T is a linear transformation by verifying the two linear transformation axioms (b) Determine the standard matrix representation for T. (c) Give a...