1. Prove that the following are invertible transformations and compute theirinverse:(a) T: R2 – R2, T (x, y) = (x + Y, x).(b) T : R2 – R?, T (x, y) = (y, x).(c) T: R2 → R?, T (x, y) = (2x + y, 3x – y).(d) T: R3 - R³, T (x, y, z) = (x +y + 2, x – y, y + z).In all these examples, write the matrix of T and the matrix of itsinverse T-1 and verify that their multiplication is the unit matrix.>

Answered: Image /qna-images/answer/d69cb19b-c7a9-418f-9620-8fd88e6b66b9.jpg

1. Prove that the following are invertible transformations and compute their inverse: (a) T: R2 → R², T (x, y) = (x + y, æ). (b) T : R2 – R?, T (x, y) = (y, x). (c) T: R? → R², T (x, y) = (2x + y, 3x – y). (d) T: R³ → R³, T (x, y, z) = ( + y+ z, x – y, Y + z). In all these examples, write the matrix of T and the matrix of its inverse T-l and verify that their multiplication is the unit matrix. |3D |

1. Prove that the following are invertible transformations and compute their inverse: (a) T: R2 → R², T (x, y) = (x + y, æ). (b) T : R2 – R?, T (x, y) = (y, x). (c) T: R? → R², T (x, y) = (2x + y, 3x – y). (d) T: R³ → R³, T (x, y, z) = ( + y+ z, x – y, Y + z). In all these examples, write the matrix of T and the matrix of its inverse T-l and verify that their multiplication is the unit matrix. |3D |

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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