Standard basis Let ēj = (1,0,0)", ē2 = (0, 1,0)", ēz = (0,0, 1)" be the standard basis of R3. Consider a linearmap T : R³ → R³ satisfying T ((x, y, z)²) = (0, 0, 0)" whenever 2x – y + z = 0.(a)-Shew that T(o, 1)7)–(0,0,0)" and T ((0,1,17)-(0,0,0)7.(b) Jstify whether T is en isomerphiem using result from (a)|(c) Given T(ē3) = (1,2, 3)". Find T (ei) and T (ē2) by using result from (a).

Given e1→=1,0,0T, e2→=0,1,0T, e3→=0,0,1T be the standard basis of ℝ3.Linear Map T: R3→R3 satisfying…

Answered: Let ēj = (1,0,0)T, ē2 = (0, 1,0)", ēz =…

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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Standard basis

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$Given \vec{e_{1}} = {(1, 0, 0)}^{T}, \vec{e_{2}} = {(0, 1, 0)}^{T}, \vec{e_{3}} = {(0, 0, 1)}^{T} be the standard basis of ℝ^{3} . Linear Map T : R^{3} \to R^{3} satisfying T ({(x, y, z)}^{T}) = {(0, 0, 0)}^{T} whenever 2 x - y + z = 0 . Given, T (\vec{e_{3}}) = {(1, 2, 3)}^{T} . Find T (\vec{e 1}) and T (\vec{e_{2}}) by using result (a) . Result (a) : T ({(\frac{1}{2}, 0, 1)}^{T}) = {(0, 0, 0)}^{T} and T ({(0, 1, 1)}^{T}) = {(0, 0, 0)}^{T}$