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In line to the standard basis for R³, the matrix of the linear operator T:R³ R³ is -3 -2 -2 A= 0 1 0 4 2 3 a. Give a formula for T(x,y,z). b. Show that T is an isomorphism and find a formula for T-¹(x,y,z). c. With respect to the basis B = {(1, -1, -1), (1, 0, 2), (1,0, -1)} for R³ find the matrix of T relative to B.

In line to the standard basis for R³, the matrix of the linear operator T:R³ R³ is -3 -2 -2 A= 0 1 0 4 2 3 a. Give a formula for T(x,y,z). b. Show that T is an isomorphism and find a formula for T-¹(x,y,z). c. With respect to the basis B = {(1, -1, -1), (1, 0, 2), (1,0, -1)} for R³ find the matrix of T relative to B.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 51E: Define T:M2,3M3,2 by T(A)=AT. aFind the matrix for T relative to the standard bases for M2,3 and...
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Sample Problem: Show all necessary solution. In line to the standard basis for R³, the matrix of the linear operator T:R³ R³ is -3 -2 -2 A= 0 1 0 4 2 3 a. Give a formula for T(x,y,z). b. Show that T is an isomorphism and find a formula for T-¹(x,y,z). c. With respect to the basis B = {(1, -1, -1), (1, 0, 2), (1,0, -1)} for R³ find the matrix of T relative to B.
Transcribed Image Text:Sample Problem: Show all necessary solution. In line to the standard basis for R³, the matrix of the linear operator T:R³ R³ is -3 -2 -2 A= 0 1 0 4 2 3 a. Give a formula for T(x,y,z). b. Show that T is an isomorphism and find a formula for T-¹(x,y,z). c. With respect to the basis B = {(1, -1, -1), (1, 0, 2), (1,0, -1)} for R³ find the matrix of T relative to B.
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