3. Let T: U - U be a linear transformation and let Bbe a basis of U. Define the determinant det(T) of T as det(T) = det(Fla). i.e. that it does not depend on the choice of the Show that det(T) is well-defined, Prove that T is invertible if and only if det(T)メO. If T is invertible, show that basis B det(71) = det(T)

3. Let T: U - U be a linear transformation and let Bbe a basis of U. Define the determinant det(T) of T as det(T) = det(Fla). i.e. that it does not depend on the choice of the Show that det(T) is well-defined, Prove that T is invertible if and only if det(T)メO. If T is invertible, show that basis B det(71) = det(T)

Name: Please help! 3. Let T: U - U be a linear transformation and let Bbe a
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Description: Please help! 3. Let T: U - U be a linear transformation and let Bbe a basis of U. Define the determinantdet(T) of T asdet(T) = det(Fla).i.e. that it does not depend on the choice of theShow that det(T) is well-defined,Prove that T is invertible if an

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 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...

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