Which of the following functions are linear transformations T : IR3 → IR2 and which are not? (1) T(x, y, z) =(x + y + z, 0,0). (2) T(x, y, z) = (y, z, x). (3) T(x, y, z) =(x + Y + z, 1, -1). (4) T(x, y, z) =(xyz, 0, 0)

Which of the following functions are linear transformations T : IR3 → IR2 and which are not? (1) T(x, y, z) =(x + y + z, 0,0). (2) T(x, y, z) = (y, z, x). (3) T(x, y, z) =(x + Y + z, 1, -1). (4) T(x, y, z) =(xyz, 0, 0)

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 16CM

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Question

Which of the following functions are linear transformations T : IR3 → IR2 and which are not?
(1) T(x, y, z) =(x + y + z, 0,0).
(2) T(x, y, z) = (y, z, x).
(3) T(x, y, z) =(x + Y + z, 1, -1).
(4) T(x, y, z) =(xyz, 0, 0)

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