Find the unique Möbius transformation that sends 13, 0, and
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![Recall the definition of a Möbius transformation.
Find the unique Möbius transformation that sends 1→ 3, i → 0, and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55d425c7-dc72-45ef-bec6-7e38b4e50bb4%2Fe7728274-cde2-43a7-b9a4-b49b3f9f041d%2Foyqk5rb_processed.jpeg&w=3840&q=75)
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- Let T be a linear transformation from R2 into R2 such that T(1,1)=(2,3) and T(0,2)=(0,8). Find T(2,4).Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.
- Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and nullity of T. (b) Find a basis for the kernel of T.Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a T(4,4) for =45, b T(4,4) for =30, and c T(5,0) for =120.For the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the preimage of (0,0). Linear Transformation Given by a Matrix In Exercises 33-38, define the linear transformations T:RnRm by T(v)=Av. Find the dimensions of Rn andRm. A=[0110]
- For the linear transformation from Exercise 38, find a T(0,1,0,1,0), and b the preimage of (0,0,0), c the preimage of (1,1,2). Linear Transformation Given by a Matrix In Exercises 33-38, define the linear transformation T:RnRmby T(v)=Av. Find the dimensions of Rnand Rm. A=[020201010112221]In Exercises 1 and 2, determine whether the function is a linear transformation. T:M2,2R, T(A)=|A+AT|Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a the kernel of T and b the range of T. c Determine the rank and nullity of T.
- 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.For the linear transformation from Exercise 45, let =45 and find the preimage of v=(1,1). 45. Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a T(4,4) for =45, b T(4,4) for =30, and c T(5,0) for =120.
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