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8. Consider the following basis for R²: B = {[ 3 ] · [²]} Let T: R² → R² be a linear transformation defined by T(v) = Av, where A is the matrix Find [T]B. [33]. -1 25

8. Consider the following basis for R²: B = {[ 3 ] · [²]} Let T: R² → R² be a linear transformation defined by T(v) = Av, where A is the matrix Find [T]B. [33]. -1 25

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 12CM
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Find [T], [T]G, and [T]. 8. Consider the following basis for R²: 1 2 B = {[ 3 ] - [ 3 ]} 4 Let T : R² → R² be a linear transformation defined by T(v) = Av, where A is the matrix Find [T]B. 9. Let T be the linear transformation T : P3 → R³ defined by is a basis of R³. 2 [33] 5 T(a+bx+cx² + dx³) B = B Find [T], where E = {1, x, x², x³} is the standard basis of P3 and E = 3a + d -2c + b a + c 1 0 -{8.84]} 0 0 1. 1
Transcribed Image Text:Find [T], [T]G, and [T]. 8. Consider the following basis for R²: 1 2 B = {[ 3 ] - [ 3 ]} 4 Let T : R² → R² be a linear transformation defined by T(v) = Av, where A is the matrix Find [T]B. 9. Let T be the linear transformation T : P3 → R³ defined by is a basis of R³. 2 [33] 5 T(a+bx+cx² + dx³) B = B Find [T], where E = {1, x, x², x³} is the standard basis of P3 and E = 3a + d -2c + b a + c 1 0 -{8.84]} 0 0 1. 1
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