Let T: R* - R be the linear transformation represented by T(x) = Ax, where 1 -2 1 0 A = 0 1 2 4 0 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 one-to-one since the ker(T) = {0}. O Tis not one-to-one since the ker(T) = {0}. O Tis not one-to-one since the ker(T) = (0}. Tis not one-to-one since the rank(T) = {0}. O Tis one-to-one since the ker(T) = {0}.

Let T: R* - R be the linear transformation represented by T(x) = Ax, where 1 -2 1 0 A = 0 1 2 4 0 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 one-to-one since the ker(T) = {0}. O Tis not one-to-one since the ker(T) = {0}. O Tis not one-to-one since the ker(T) = (0}. Tis not one-to-one since the rank(T) = {0}. O Tis one-to-one since the ker(T) = {0}.

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 39E: For the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the...

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