(3) Consider the linear map T : R² → R² which sends (1,0) → (-3, 5) and (0, 1) →(4, – 1).(a) What is the matrix of the transformation? What is the change of coordinatesmatrix? Do they agree? How come?

Answered: Consider the linear map T : R² → R²…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.3: Matrices For Linear Transformations

Problem 44E: Let T:P2P4 be the linear transformation T(p)=x2p. Find the matrix for T relative to the bases...

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Similar questions

Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
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.
Let T:P2P3 be the linear transformation T(p)=xp. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3}.
Let T:P2P4 be the linear transformation T(p)=x2p. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3,x4}.
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Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.
Find the linear fractional transformation that maps (1,i,-1) to (-1,i,1).
Let f be the linear transformation represented by the matrix A = 4-(32) Find the point (x, y) such that f(x, y) = (-4,-1). (Give your answer exactly, not as a decimal approximation.) The point is
(3) Consider the linear map T : R² → R² which sends (1,0) → (-3, 5) and (0,1) → (4, –1). (a) What is the matrix of the transformation? What is the change of coordinates matrix? Do they agree? How come? (b) Where does this transformation send the area between the vector (4, 2) and the X-axis? Explain algebraically and draw a picture. (c) What is the image of the lower half plane under T? Explain algebraically and draw a picture. (d) What is the pre-image of the upper half plane under T? Explain algebraically and draw a picture. (e) What is the image of the unit circle under T? Explain algebraically and draw a picture. (f) Deduce whether or not linear transformations preserve angles/areas/curves/shapes, 6, etc.

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Consider the linear map T : R² → R² which sends (1,0) → (-3, 5) and (0, 1) → (4, –1). (a) What is the matrix of the transformation? What is the change of coordinates matrix? Do they agree? How come?