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Let T be a linear transformation from R³ to R² defined by T(x, y, z) = (2x + y + z, x − y − z) (*) a) Find the matrix of T with respect to the bases B₁ = {(1,-1, 1), (1, 2, -3), (-2, 1, -1)} and B₂ = {(1, -2), (1,-1)}. b) Use the matrix found in part a) to find T(v), where (v) B₁ = (2, 1, 1) hence v = (1, 1, -2). Compare this with the result you obtain by using formula (*).

Let T be a linear transformation from R³ to R² defined by T(x, y, z) = (2x + y + z, x − y − z) (*) a) Find the matrix of T with respect to the bases B₁ = {(1,-1, 1), (1, 2, -3), (-2, 1, -1)} and B₂ = {(1, -2), (1,-1)}. b) Use the matrix found in part a) to find T(v), where (v) B₁ = (2, 1, 1) hence v = (1, 1, -2). Compare this with the result you obtain by using formula (*).

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...
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Let T be a linear transformation from R³ to R2 defined by T(x, y, z) = (2x + y + z, x-y-z) (*) a) Find the matrix of T with respect to the bases B₁ = {(1,-1, 1), (1, 2, -3), (-2, 1,-1)} and B₂ = {(1, −2), (1, -1)}. b) Use the matrix found in part a) to find 7(v), where (v) B₁ = (2,1,1) hence v = (1,1,-2). Compare this with the result you obtain by using formula (*).
Transcribed Image Text:Let T be a linear transformation from R³ to R2 defined by T(x, y, z) = (2x + y + z, x-y-z) (*) a) Find the matrix of T with respect to the bases B₁ = {(1,-1, 1), (1, 2, -3), (-2, 1,-1)} and B₂ = {(1, −2), (1, -1)}. b) Use the matrix found in part a) to find 7(v), where (v) B₁ = (2,1,1) hence v = (1,1,-2). Compare this with the result you obtain by using formula (*).
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