Explanation Given: Linear transformation T defined by T ( f ) = f ( 2 t ) from P 2 to P 2 Where f ( t ) is a polynomial of degree at least 2 and basis of P 2 is β = { 1 , t , t 2 } . Concept Used: Let T be a linear transformation defined from R 2 to R 2 then And e 1 = [ 1 0 ] , e 2 = [ 0 1 ] be the standard bases of R 2 then every element of range of T can be written as linear combination of e 1 = [ 1 0 ] and e 2 = [ 0 1 ] , T ( e 1 ) = a e 1 + b e 2 T ( e 2 ) = c e 1 + d

Linear Algebra with Applications (2-Download)

5th Edition

ISBN: 9780321796974

Author: Otto Bretscher

Publisher: PEARSON

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Chapter 4.3, Problem 26E

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The matrix A representing a linear transformation T defined by T(f)=f(2t) from P2 to P2 with respect to the basis β={1,t,t2}

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Chapter 4.3, Problem 25E

Chapter 4.3, Problem 27E

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Chapter 4 Solutions

Linear Algebra with Applications (2-Download)

Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...

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The matrix A representing a linear transformation T defined by T ( f ) = f ( 2 t ) from P 2 to P 2 with respect to the basis β = { 1 , t , t 2 }

Solution Summary: The author explains that the matrix A representing a linear transformation T is given by f(2t).

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The matrix A representing a linear transformation T defined by T(f)=f(2t) from P2 to P2 with respect to the basis β={1,t,t2}

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Chapter 4 Solutions