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)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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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