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1. Prove whether or not the following are linear transformations. Make sure to provide a specific counter- example of a failed property when possible. (a) Let A = Rmxn, and consider the transformation T: R R defined by T(x) = Ax. (b) Let WP₁ and Consider the transformation T: VW defined by V = {ax²+(3a2b)x+b|a, bER} CP2. T(ax² + (3a-2b)x + b) = 2ax +3a-2b.

1. Prove whether or not the following are linear transformations. Make sure to provide a specific counter- example of a failed property when possible. (a) Let A = Rmxn, and consider the transformation T: R R defined by T(x) = Ax. (b) Let WP₁ and Consider the transformation T: VW defined by V = {ax²+(3a2b)x+b|a, bER} CP2. T(ax² + (3a-2b)x + b) = 2ax +3a-2b.

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.CR: Review Exercises
Problem 21CR: Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find...
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1. Prove whether or not the following are linear transformations. Make sure to provide a specific counter- example of a failed property when possible. (a) Let A = Rmxn, and consider the transformation T: R R defined by T(x) = Ax. (b) Let WP₁ and Consider the transformation T: VW defined by V = {ax²+(3a2b)x+b|a, bER} CP2. T(ax² + (3a-2b)x + b) = 2ax +3a-2b.
Transcribed Image Text:1. Prove whether or not the following are linear transformations. Make sure to provide a specific counter- example of a failed property when possible. (a) Let A = Rmxn, and consider the transformation T: R R defined by T(x) = Ax. (b) Let WP₁ and Consider the transformation T: VW defined by V = {ax²+(3a2b)x+b|a, bER} CP2. T(ax² + (3a-2b)x + b) = 2ax +3a-2b.
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