Let B = {(1, 0, 0),(1, 1, 0),(1, 1, 1)} and B'= {(1, 1, 1),(0, 1, 1),(0, 0, 1)}. It can be shown that B is a basis for R3 . Let T be a linear operator on R3 such that the matrix of T with respect to the basis B is [T]B = 1 2 3 0 4 5 0 0 6 Find the matrix [T]B' of T with respect to the basis B'. Justify your answer

Let B = {(1, 0, 0),(1, 1, 0),(1, 1, 1)} and B'= {(1, 1, 1),(0, 1, 1),(0, 0, 1)}. It can be shown that B is a basis for R3 . Let T be a linear operator on R3 such that the matrix of T with respect to the basis B is [T]B = 1 2 3 0 4 5 0 0 6 Find the matrix [T]B' of T with respect to the basis B'. Justify your answer

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 18CM

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Question

Let B = {(1, 0, 0),(1, 1, 0),(1, 1, 1)} and B'= {(1, 1, 1),(0, 1, 1),(0, 0, 1)}. It can be
shown that B is a basis for R³. Let T be a linear operator on R³ such that the matrix of T with respect to the basis B is

[T]_{B =} 1 2 3 0 4 5 0 0 6

Find the matrix [T]_B' of T with respect to the basis B'. Justify your answer.

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