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6. Let T : Rª –→ Rª be given by T((x1,x2, x3, x4)) = (x1 – 2, x2 – x1,0, x3 + x4). It is known that T is a linear transformation (you DO NOT have to show this fact). (a) ( Find the kernel of T. (b) : Prove or disprove: T is a one-to-one linear transformation. NOTE: You must show work to back up your answer. Answers without any work will receive no credit.

6. Let T : Rª –→ Rª be given by T((x1,x2, x3, x4)) = (x1 – 2, x2 – x1,0, x3 + x4). It is known that T is a linear transformation (you DO NOT have to show this fact). (a) ( Find the kernel of T. (b) : Prove or disprove: T is a one-to-one linear transformation. NOTE: You must show work to back up your answer. Answers without any work will receive no credit.

Elementary Linear Algebra (MindTap Course List)
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 12CM
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6. Let T : R4 → R4 be given by T((x1, x2, x3, x4)) = (x1 – x2, x2 – x1,0, x3 + x4). It is known that T is a linear transformation (you DO NOT have to show this fact). (a) ( Find the kernel of T. (b) : Prove or disprove: T is a one-to-one linear transformation. NOTE: You must show work to back up your answer. Answers without any work will receive no credit.
Transcribed Image Text:6. Let T : R4 → R4 be given by T((x1, x2, x3, x4)) = (x1 – x2, x2 – x1,0, x3 + x4). It is known that T is a linear transformation (you DO NOT have to show this fact). (a) ( Find the kernel of T. (b) : Prove or disprove: T is a one-to-one linear transformation. NOTE: You must show work to back up your answer. Answers without any work will receive no credit.
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