(I) Find the fractional linear transformation f such that f(0) 2 – 2i, f(1) = 0 and f(∞) = -2 – 2i. (II) Find the images of x-axis and y-axis mapped by f.
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Q: 1) Sketch the graph of f(x) = 2(x + 3)² using standard transformation techniques.
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Q: Find the image of any point on x^2+y^2=4 under the transformation (x,y)-->(1/2x,1/2y).
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Q: 2 Find the standard matrix for the linear transformation T:R² → R² that rotates points about the…
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Q: Find the standard matrix for the linear transformation T:R² → R² that rotates points about the…
A: Explanation of the answer is as follows
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- A translation in R2 is a function of the form T(x,y)=(xh,yk), where at least one of the constants h and k is nonzero. (a) Show that a translation in R2 is not a linear transformation. (b) For the translation T(x,y)=(x2,y+1), determine the images of (0,0,),(2,1), and (5,4). (c) Show that a translation in R2 has no fixed points.Find range R(T) of linear transformation T(x1,x2,x3)=(x1-x2,x1+x3)determine the critical point x = x0, and then classify its type and examine its stability by making the transformation x = x0 + u. 13.(0−βδ0)+(α−γ);α,β,γ,δ>0
- Find the image of any point on x^2+y^2=4 under the transformation (x,y)-->(1/2x,1/2y).A linear transformation F from R2 to R2 is defined as the projection onto the x−axis, followed by the rotation counterclockwise by π/3 , followed by the projection onto the y−axis. Find the matrix of F.Give an example of a linear transformation T: R2 --> R2 such that N(T) = R(T).
- Determine whether the linear transformation is invertible. If it is, finds its inverse. a) T(x,y) = (x+y, 2y+2x) b) T(x,y) = (x+y, 2y-x)Determine whether the linear transformation is invertible. If it is, find its inverse.T(x, y) = (2x, 0)Find the linear fractional transformation that maps (1,i,-1) to (-1,i,1).