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Let 7: R" → RS be he linear transformation represented by T(x) = Ax, where %3D 1 -2 3 0 A = 1 2 1 0 0 1 %3D

Let 7: R" → RS be he linear transformation represented by T(x) = Ax, where %3D 1 -2 3 0 A = 1 2 1 0 0 1 %3D

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 41E
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E Apps Bb Welcome, ARYA - B... PMyEnglishLab Desmos | Graphing... MyBenefits CalWIN M Quadratic Equation... (3 unread) - aryaha.. O Selective Serv ... Let T: R → R be the linear transformation represented by T(x) = Ax, where %3D 1 2 3 0 A = 1 2 1 0 0 1 (a) Find the dimension of the domain. (b) Find the dimension of the range. (c) Find the dimension of the kernel. (d) Is T one-to-one? Explain. O Tis not one-to-one since the ker(T) = {0}. O Tis not one-to-one since the rank(T) {0}. O Tis not one-to-one since the ker(T) ± {0}. O Tis one-to-one since the ker(7) ± {0}. O Tis one-to-one since the ker(T) = {0}. (e) Is T onto? Explain. O T is onto since the rank(T) is equal to the dimension of the domain. O Tis not onto since the rank(T) is not equal to the dimension of the domain. O Tis not onto since the rank(7) is not equal to the dimension of the range. O Tis not onto since the rank(7) is equal to the dimension of the range. O Tis onto since the rank(T) is equal to the dimension of the range. (f) Is T an isomorphism? Explain. (Select all that apply.) OT is not an isomorphism since it is not onto. U T is an isomorphism since it is one-to-one and onto. Tyne hero to conrch
Transcribed Image Text:E Apps Bb Welcome, ARYA - B... PMyEnglishLab Desmos | Graphing... MyBenefits CalWIN M Quadratic Equation... (3 unread) - aryaha.. O Selective Serv ... Let T: R → R be the linear transformation represented by T(x) = Ax, where %3D 1 2 3 0 A = 1 2 1 0 0 1 (a) Find the dimension of the domain. (b) Find the dimension of the range. (c) Find the dimension of the kernel. (d) Is T one-to-one? Explain. O Tis not one-to-one since the ker(T) = {0}. O Tis not one-to-one since the rank(T) {0}. O Tis not one-to-one since the ker(T) ± {0}. O Tis one-to-one since the ker(7) ± {0}. O Tis one-to-one since the ker(T) = {0}. (e) Is T onto? Explain. O T is onto since the rank(T) is equal to the dimension of the domain. O Tis not onto since the rank(T) is not equal to the dimension of the domain. O Tis not onto since the rank(7) is not equal to the dimension of the range. O Tis not onto since the rank(7) is equal to the dimension of the range. O Tis onto since the rank(T) is equal to the dimension of the range. (f) Is T an isomorphism? Explain. (Select all that apply.) OT is not an isomorphism since it is not onto. U T is an isomorphism since it is one-to-one and onto. Tyne hero to conrch
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