Explanation Given: The given condition is, T : R 2 → R 2 : T ( x , y ) = ( 5 x + 4 y , 4 x + 5 y ) B ′ = { ( 12 , − 13 ) , ( 13 , − 12 ) } Procedure used: A , A ′ , P and P − 1 representation: Matrix for T relative to B : A Matrix for T relative to B ′ : A ′ Transition matrix from B ′ to B : P Transition matrix from B to B ′ : P − 1 Transition matrix from B ′ to B: It determine by changing the [ B B ′ ] into [ I P ] : Transition matrix from B to B ′ : It determine by changing the [ B ′ B ] into [ I P − 1 ] : Calculation: Consider the given condition, T : R 2 → R 2 : T ( x , y ) = ( 5 x + 4 y , 4 x + 5 y ) B ′ = { ( 12 , − 13 ) , ( 13 , − 12 ) } The standard matrix for T by using the coefficient of x and y is, A = [ 5 4 4 5 ] Consider the standard basis B : B = { ( 1 , 0 ) , ( 0 , 1 ) } Find the transition matrix from B to B ′ by changing [ B ′ B ] into [ I P − 1 ] : [ 12 13 1 0 − 13 − 12

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN: 9781305658004

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6.4, Problem 6E

To determine

To find:

The matrix A′ for T:R2→R2:T(x,y)=(5x+4y,4x+5y) and B′={(12,−13),(13,−12)}.

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Chapter 6.4, Problem 5E

Chapter 6.4, Problem 7E

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The matrix A ′ for T : R 2 → R 2 : T ( x , y ) = ( 5 x + 4 y , 4 x + 5 y ) and B ′ = { ( 12 , − 13 ) , ( 13 , − 12 ) } .

Solution Summary: The author explains how to find the matrix Aprime for the given condition.

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To find:

The matrix A′ for T:R2→R2:T(x,y)=(5x+4y,4x+5y) and B′={(12,−13),(13,−12)}.

Want to see the full answer?

Chapter 6 Solutions

The matrix A ′ for T : R 2 → R 2 : T ( x , y ) = ( 5 x + 4 y , 4 x + 5 y ) and B ′ = { ( 12 , − 13 ) , ( 13 , − 12 ) } .

Solution Summary: The author explains how to find the matrix Aprime for the given condition.

Videos

To find: The matrix A′ for T:R2→R2:T(x,y)=(5x+4y,4x+5y) and B′={(12,−13),(13,−12)}.

Want to see the full answer?

Chapter 6 Solutions

To find:

The matrix A′ for T:R2→R2:T(x,y)=(5x+4y,4x+5y) and B′={(12,−13),(13,−12)}.