Let B={v_1...v_n} be a basis for R^n and let E be a standard basis for R^n. Let T: R^n ->R^n be the change of basis transformation T({x}b ) ={x}E . Prove that T is a bijection. (T is a matrix transformation).
Let B={v_1...v_n} be a basis for R^n and let E be a standard basis for R^n. Let T: R^n ->R^n be the change of basis transformation T({x}b ) ={x}E . Prove that T is a bijection. (T is a matrix transformation).
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 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...
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Let B={v_1...v_n} be a basis for R^n and let E be a standard basis for R^n. Let T: R^n ->R^n be the change of basis transformation T({x}b ) ={x}E . Prove that T is a bijection.
(T is a matrix transformation).
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Further follows,
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