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6. Let {V1, V2,..., Un} be a basis for Rn. Let T: RnRn be a linear transformation which is one-one and onto. (a) Prove that {Tv₁, Tv2, ....., Tvn} is also a basis for R". (b) If T is only one-one but not onto then is {TV₁, TV2, basis for R? Explain. ....., Tun} a

6. Let {V1, V2,..., Un} be a basis for Rn. Let T: RnRn be a linear transformation which is one-one and onto. (a) Prove that {Tv₁, Tv2, ....., Tvn} is also a basis for R". (b) If T is only one-one but not onto then is {TV₁, TV2, basis for R? Explain. ....., Tun} 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 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...
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6. Let {V1, V2, Vn} be a basis for R". Let T : R" → R" be a linear .....) transformation which is one-one and onto. (a) Prove that {Tv1,Tv2, Tvn} is also a basis for R". .....) (b) If T is only one-one but not onto then is {Tv1,Tv2, .., Tvn} a basis for R"? Explain. ......
Transcribed Image Text:6. Let {V1, V2, Vn} be a basis for R". Let T : R" → R" be a linear .....) transformation which is one-one and onto. (a) Prove that {Tv1,Tv2, Tvn} is also a basis for R". .....) (b) If T is only one-one but not onto then is {Tv1,Tv2, .., Tvn} a basis for R"? Explain. ......
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