10. Consider the transformation T : R4 → Rª defined byT(x1, 12, X3, x4) = (x4, 0, x2,0)(a) Find the associated matrix for T.(b) Find a basis for ker(T).(c) Find a basis for R(T) (Range).(d) Is T an isomorphism?

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Answered: 10. Consider the transformation T : R4…

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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[2] such that 7(6₁)=56, +46, and 7(6₂)=35, +56₂. Let == B= and ba = (a) The 28-matrix of T (in other words, the matrix of T relative to the basis 33) is 5 3 A= The set = {1,5} is a basis for R². Let T: R2 R² be a linear transformation → 5 (b) The standard matrix of 7 (in other words, the matrix of T relative to the standard basis for R²) is -1 You have answered these types of questions (in b) before. Can you now use coordinates and the A-SBS-¹ framework? Which technique do you prefer?
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10. Consider the transformation T : R4 → Rª defined by T(x1, 12, X3, x4) = (x4, 0, x2,0) (a) Find the associated matrix for T. (b) Find a basis for ker(T). (c) Find a basis for R(T) (Range). (d) Is T an isomorphism?