Let 1 : D 1 D 2 and 2 : D 2 D
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Let Φ1 : D1 → D2 and Φ2 : D2 → D3 be C1 maps, and let Φ2 ◦ Φ1 : D1 → D3 be the composite map. Use the Multivariable Chain Rule and Exercise 49 to show that
Data From Exercise 49
The product of 2 × 2 matrices A and B is the matrix AB defined by
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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