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3) Let T a) b) C) d) a b = abcd + abcx + abx². : This transformation maps the zero vector to a zero vector. : This transformation is closed under addition. If this is false, a counterexample is given by: u = : This transformation is closed under scalar multiplication. If this is false, a counterexample is given by: u = : This transformation is a linear transformation. and U = and k =

3) Let T a) b) C) d) a b = abcd + abcx + abx². : This transformation maps the zero vector to a zero vector. : This transformation is closed under addition. If this is false, a counterexample is given by: u = : This transformation is closed under scalar multiplication. If this is false, a counterexample is given by: u = : This transformation is a linear transformation. and U = and k =

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 34EQ
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3) Let T b) O a +11 이 = abcd + abcx + abx². : This transformation maps the zero vector to a zero vector. : This transformation is closed under addition. his is false, a counterexample is given by: u = : This transformation is closed under scalar multiplication. If this is false, a counterexample is given by: u = : This transformation is a linear transformation. and U = and k = U
Transcribed Image Text:3) Let T b) O a +11 이 = abcd + abcx + abx². : This transformation maps the zero vector to a zero vector. : This transformation is closed under addition. his is false, a counterexample is given by: u = : This transformation is closed under scalar multiplication. If this is false, a counterexample is given by: u = : This transformation is a linear transformation. and U = and k = U
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