Explanation Approach: The matrix A ′ is obtain as, A ′ [ v ] B ′ = [ T ( v ) ] B ′ And, other way to obtain A ′ is by using the matrices P , A and P − 1 as, P − 1 A P [ v ] B ′ = [ T ( v ) ] B ′ This implies that A ′ = P − 1 A P . Calculation: Consider the given condition: T : R 3 → R 3 , T ( x , y , z ) = ( x , x + 2 y , x + y + 3 z ) B ′ = { ( 1 , − 1 , 0 ) , ( 0 , 0 , 1 ) , ( 0 , 1 , − 1 ) } The standard matrix for T by using the coefficient of x , y and z : A = [ 1 0 0 1 2 0 1 1 3 ] Consider the standard basis B : B = { ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , ( 0 , 0 , 1 ) } Find the transition matrix from B to B ′ by changing [ B ′ B ] into [ I P − 1 ] : [ 1 0 0 1 0 0 − 1 0 1 0 1 0 0 1 − 1 0 0 1 ] → [ 1 0 0 1 0 0 0 1 0 1 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 12E

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To find:

The matrix A′ for the linear transformation T:R3→R3, T(x,y,z)=(x,x+2y,x+y+3z) relative to the basis B′={(1,−1,0),(0,0,1),(0,1,−1)}.

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Chapter 6.4, Problem 11E

Chapter 6.4, Problem 13E

Chapter 6 Solutions

Elementary Linear Algebra (MindTap Course List)

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The matrix A ′ for the linear transformation T : R 3 → R 3 , T ( x , y , z ) = ( x , x + 2 y , x + y + 3 z ) relative to the basis B ′ = { ( 1 , − 1 , 0 ) , ( 0 , 0 , 1 ) , ( 0 , 1 , − 1 ) } .

Solution Summary: The author explains how to obtain the matrix Aprime for the linear transformation T by using the matrices P, A and

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To find:

The matrix A′ for the linear transformation T:R3→R3, T(x,y,z)=(x,x+2y,x+y+3z) relative to the basis B′={(1,−1,0),(0,0,1),(0,1,−1)}.

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Chapter 6 Solutions

The matrix A ′ for the linear transformation T : R 3 → R 3 , T ( x , y , z ) = ( x , x + 2 y , x + y + 3 z ) relative to the basis B ′ = { ( 1 , − 1 , 0 ) , ( 0 , 0 , 1 ) , ( 0 , 1 , − 1 ) } .

Solution Summary: The author explains how to obtain the matrix Aprime for the linear transformation T by using the matrices P, A and

Videos

To find: The matrix A′ for the linear transformation T:R3→R3, T(x,y,z)=(x,x+2y,x+y+3z) relative to the basis B′={(1,−1,0),(0,0,1),(0,1,−1)}.

Want to see the full answer?

Chapter 6 Solutions

To find:

The matrix A′ for the linear transformation T:R3→R3, T(x,y,z)=(x,x+2y,x+y+3z) relative to the basis B′={(1,−1,0),(0,0,1),(0,1,−1)}.