Explanation Given: The given condition is: T : R 2 → R 2 : T ( x , y ) = ( − 3 x + y , 3 x − y ) B ′ = { ( 1 , − 1 ) , ( − 1 , 5 ) } 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 ) = ( − 3 x + y , 3 x − y ) B ′ = { ( 1 , − 1 ) , ( − 1 , 5 ) } The standard matrix for T by using the coefficient of x and y : A = [ − 3 1 3 − 1 ] 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 ] :

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN: 9781305658004

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6.4, Problem 5E

To determine

To find:

The matrix A′ for T:R2→R2:T(x,y)=(−3x+y,3x−y) and B′={(1,−1),(−1,5)}.

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Chapter 6.4, Problem 4E

Chapter 6.4, Problem 6E

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Chapter 6 Solutions

Elementary Linear Algebra (MindTap Course List)

Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Prob. 4E Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Linear TransformationsIn Exercises 9-22, determine...Ch. 6.1 - Linear TransformationsIn Exercises 9-22, determine...

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The matrix A ′ for T : R 2 → R 2 : T ( x , y ) = ( − 3 x + y , 3 x − y ) and B ′ = { ( 1 , − 1 ) , ( − 1 , 5 ) } .

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)=(−3x+y,3x−y) and B′={(1,−1),(−1,5)}.

Want to see the full answer?

Chapter 6 Solutions

The matrix A ′ for T : R 2 → R 2 : T ( x , y ) = ( − 3 x + y , 3 x − y ) and B ′ = { ( 1 , − 1 ) , ( − 1 , 5 ) } .

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)=(−3x+y,3x−y) and B′={(1,−1),(−1,5)}.

Want to see the full answer?

Chapter 6 Solutions

To find:

The matrix A′ for T:R2→R2:T(x,y)=(−3x+y,3x−y) and B′={(1,−1),(−1,5)}.