) Let T: P1 (R) -› P2 (R) be the linear transformation defined by T(2t + 1) = t^2 - 1 and T(2t - 1) = t^2 + t. Find T(at + b) b) Let L: R^2 -> R^3 be the linear transformation given by L(x,y) = (x,x + y, y). i) Find ker(L) ii) is L 1-1 iii) is L onto

) Let T: P1 (R) -› P2 (R) be the linear transformation defined by T(2t + 1) = t^2 - 1 and T(2t - 1) = t^2 + t. Find T(at + b) b) Let L: R^2 -> R^3 be the linear transformation given by L(x,y) = (x,x + y, y). i) Find ker(L) ii) is L 1-1 iii) is L onto

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 3CM: Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions...

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a) Let T: P1 (R) -› P2 (R) be the linear transformation defined by T(2t + 1) = t^2 - 1 and T(2t - 1) = t^2 + t. Find T(at + b) b) Let L: R^2 -> R^3 be the linear transformation given by L(x,y) = (x,x + y, y). i) Find ker(L) ii) is L 1-1 iii) is L onto

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