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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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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