c4s2 - 4.2 The Determinant of a Square Matrix 1 Chapter 4....

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4.2 The Determinant of a Square Matrix 1 Chapter 4. Determinants 4.2 The Determinant of a Square Matrix Defnition. The minor matrix A ij of an n × n matrix A is the ( n 1) × ( n 1) matrix obtained from it by eliminating the i th row and the j th column. Example. Find A 11 , A 12 ,and A 13 for A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 . Defnition. The determinant of A ij times ( 1) i + j is the cofactor of entry a ij in A , denoted A 0 ij .
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4.2 The Determinant of a Square Matrix 2 Example. We can write determinants of 3 × 3 matrices in terms of cofactors: det( A )= ± ± ± ± ± ± ± ± ± ± a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ± ± ± ± ± ± ± ± ± ± = a 11 | A 11 |− a 12 | A 12 | + a 13 | A 13 | = a 11 a 0 11 + a 12 a 0 12 + a 13 a 0 13 . Note. The following deFnition is recursive . ±or example, in order to process the deFnition for n = 4 you must process the deFnition for n =3 , n =2 ,and n =1 . Defnition 4.1. The determinant of a 1 × 1 matrix is its single entry.
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This note was uploaded on 02/24/2012 for the course MATH 285 taught by Professor Igordolgachev during the Fall '04 term at University of Michigan-Dearborn.

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c4s2 - 4.2 The Determinant of a Square Matrix 1 Chapter 4....

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