Q.4) Let B = {v1, V2, V3, V4} be a basis for R4.Let T: R4 → Rª be the linear transformation such that on the basis vectors v1, V2, V3, V4, its values are:2v1 -2v2+2v3 +3v4+3v3T(v1)T(v2)T(v3) =T(v4) =6V1V1-V2+V4+2v2+v3-2v4Vị(e) Compute the trace of the linear operator T.(f) Compute the kernel of the linear operator T w.r.t. basis B.

Answered: Image /qna-images/answer/b09dee35-0f52-4c9f-9592-3f9aae6f9bbe.jpg

Let B = {v1, vV2, V3, V4} be a basis for R4. Let T: R4 → R be the linear transformation such that on the basis vectors v1, V2, V3, V4, its values are: T(v1) = 2v1 -2v2 +2v3 +3v4 T(v2) = 6v1 T(v3) : T(v4) = +3v3 V1 -V2 +V4 V1 +2v2 +v3 -2v4 (e) Compute the trace of the linear operator T. (f) Compute the kernel of the linear operator T w.r.t. basis B.

Let B = {v1, vV2, V3, V4} be a basis for R4. Let T: R4 → R be the linear transformation such that on the basis vectors v1, V2, V3, V4, its values are: T(v1) = 2v1 -2v2 +2v3 +3v4 T(v2) = 6v1 T(v3) : T(v4) = +3v3 V1 -V2 +V4 V1 +2v2 +v3 -2v4 (e) Compute the trace of the linear operator T. (f) Compute the kernel of the linear operator T w.r.t. basis B.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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