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Let bi = 2 and b₂ = 3 The set = •{b₁, b₂} is a basis for R2. Let T: R² → R2 be a linear transformation such that T(b₁)=4b16b2 and T(b2) = 2b₁+8b2. (a) The B-matrix of T (in other words, the matrix of T relative to the basis B) is B = (b) The standard matrix of T (in other words, the matrix of T relative to the standard basis for R²) is A =

Let bi = 2 and b₂ = 3 The set = •{b₁, b₂} is a basis for R2. Let T: R² → R2 be a linear transformation such that T(b₁)=4b16b2 and T(b2) = 2b₁+8b2. (a) The B-matrix of T (in other words, the matrix of T relative to the basis B) is B = (b) The standard matrix of T (in other words, the matrix of T relative to the standard basis for R²) is A =

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 11CM
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Let bi = 2 and b₂ = 3 The set = •{b₁, b₂} is a basis for R2. Let T: R² → R2 be a linear transformation such that T(b₁)=4b16b2 and T(b2) = 2b₁+8b2. (a) The B-matrix of T (in other words, the matrix of T relative to the basis B) is B = (b) The standard matrix of T (in other words, the matrix of T relative to the standard basis for R²) is A =
Transcribed Image Text:Let bi = 2 and b₂ = 3 The set = •{b₁, b₂} is a basis for R2. Let T: R² → R2 be a linear transformation such that T(b₁)=4b16b2 and T(b2) = 2b₁+8b2. (a) The B-matrix of T (in other words, the matrix of T relative to the basis B) is B = (b) The standard matrix of T (in other words, the matrix of T relative to the standard basis for R²) is A =
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