Use Exercise 50 to prove that Verify that Jac(I) = 1, where I is the identity map

Question:

Use Exercise 50 to prove that

Jac() = Jac()-

Verify that Jac(I) = 1, where I is the identity map I(u, v) = (u, v).


Data From Exercise 50

Let Φ1 : D→ D2 and Φ2 : D→ D3 be C1 maps, and let Φ◦ Φ1 : D1 → D3 be the composite map. Use the Multivariable Chain Rule and Exercise 49 to show that

Jac(D0 D) Jac()Jac()


Data From Exercise 49

The product of 2 × 2 matrices A and B is the matrix AB defined by

a b b' ( 5 ) ( 2 5 ) = C d d' A B aa' + bc' ca' + de' ab' + bd' cb' + dd' AB

The (i, j)-entry of A is the dot product of the ith row of A and the jth column of B. Prove that det(AB) = det(A) det(B).

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Related Book For  book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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