If possible, teach me both question a and b, if only can help 1 question, then solve question b. Let ēj = (1,0, 0)", é2 = (0, 1, 0)", ēz = (0,0, 1)T 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) Show that T ((G,0, –1)") = (0, 0, 0)" and T (0, 1, 1)?) = (0,0,0)".-(b) Justify whether T is an isomorphism using result from (a).

Answered: Image /qna-images/answer/28e3b4c1-152f-4d58-8089-49c633f100e0.jpg

Let ēj = (1,0,0)", ē2 = (0, 1, 0)", ēz = (0,0, 1)" be the standard basis of R³. Consider a linear map T : R³ → R³ satisfying T (x, y, z)") = (0,0, 0)" whenever 2x – y + z = 0. (a) Show that T (G,0, –1)") = (0,0, 0)" and T ((0, 1, 1)") = (0, 0, 0)". (b) Justify whether T is an isomorphism using result from (a).

Let ēj = (1,0,0)", ē2 = (0, 1, 0)", ēz = (0,0, 1)" be the standard basis of R³. Consider a linear map T : R³ → R³ satisfying T (x, y, z)") = (0,0, 0)" whenever 2x – y + z = 0. (a) Show that T (G,0, –1)") = (0,0, 0)" and T ((0, 1, 1)") = (0, 0, 0)". (b) Justify whether T is an isomorphism using result from (a).

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 18CM

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