Topic is Linear Transformation: Instruction: Provide the image for v and the pre-image for u of the given linear transformation: a. T: R2 -> R2, T(v1 ,v2) = (v1 , v1 + 2v2) , where v = (2,3), u = (4,12) b. T: R3 -> R3, T(v1 , v2 , v3 ) = (0 , v1 + v2 , v2 + v3) , v = (-3,2,5) , u = (0,2,5)

Topic is Linear Transformation: Instruction: Provide the image for v and the pre-image for u of the given linear transformation: a. T: R2 -> R2, T(v1 ,v2) = (v1 , v1 + 2v2) , where v = (2,3), u = (4,12) b. T: R3 -> R3, T(v1 , v2 , v3 ) = (0 , v1 + v2 , v2 + v3) , v = (-3,2,5) , u = (0,2,5)

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 17CM

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Question

Topic is Linear Transformation:

Instruction: Provide the image for v and the pre-image for u of the given linear transformation:

a. T: R₂-> R_2, T(v₁ ,v₂) = (v₁, v₁ + 2v₂) , where v = (2,3), u = (4,12)

b. T: R₃ -> R_3, T(v1 , v2 , v₃) = (0 , v₁ + v₂ , v₂+ v₃) , v = (-3,2,5) , u = (0,2,5)

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T:R3⟶R3 with T(v1,v2,v3)=(v1+v2,v2+v3,v3). Find the a. image of v=(−2,1,2) b. pre-image of w=(0,1,2)

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