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 and only if det(T)メO. If T is invertible, show thatbasis Bdet(71) =det(T)

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Asked Mar 12, 2019
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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)
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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)

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Expert Answer

Step 1

To establish some basic facts about the determinant of a linear transformation T from U to U (U a vector space)

Step 2

A linear transformation T;U->U is a map satisfying the properties shown. 

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Step 3

Let B be a basis of U. Then T is represented as a squ...

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