Question 6 Consider the endomorphisms deifnined on p 3 by Tx,y,z) = (7x+2y+z, 3y-z, -3x+ 4y-2z): Sx,y,z) = (-2x+8y-5z, 3x-11y+7z, 9x-34y +21z) Find the composite of the endomorphisms: S-Tx, y, z)= [A] T S(x, y, z) = [B]
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- this question is differential geometry Let F: IR3 →IR3 is a diffeomorphism and M is a surface in IR3 , prove that the image F(M) is also a surface in IR3.Show that the image of the annulus {1<|z|<2} under w=2/(z-1) is the domain {W: Re(W)>-1, |W=2/3|>4/3} using Möbius transformation.Sketch the image of the unit square [a square with vertices at (0, 0), (1, 0), (1, 1), and (0, 1)] under the specified transformation.T is the expansion represented by T(x, y) = (5x, y).
- Apply the transformation T (x, y) = (0.8x − 0.6y, 0.6x + 0.8y) to the scalene triangle whose vertices are (0, 0), (5, 0), and (0, 10). What kind of isometry does T seem to be? Be as specific as you can, and provide numerical evidence for your conclusion.Find the image of any point on x^2+y^2=4 under the transformation (x,y)-->(1/2x,1/2y).Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the specified transformation.T is the expansion represented by T(x, y) = (2x, y).
- Consider the transformation T, (defined in the uv plane) given by (image) with u>0 and v>0. We can state that: there may be more than one correct option a. T sends horizontal segments in pieces of hyperbolas. b. T sends horizontal segments in line segments passing through the origin. c. T sends vertical segments in pieces of circumferences. d.T sends vertical segments in pieces of parabolas.3.2-4) (a) Prove that an isometry F = TC carries the plane through p orthogonal to q ≠ 0 to the plane through F(p) orthogonal to C(q).Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the specified transformation.T is the expansion represented by T(x, y) = (x, 6y).