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Unformatted text preview: inversions, and therefore is even. 52413 has 4 + 1 + 2 + 0 = 7 inversions, and therefore is odd. Denition 5. The sign of a permutation is (1) number of inversion in other words, it is +1 if the permutation is even and1 if the permutation is odd. Denition 6. Let A be a n n matrix. Then we dene the determinant of A : det A = X permutations j 1 ,...,j n sign a 1 ,j 1 a 2 ,j 2 a n,j n This denition may appear confusing, so we will do some examples to see what this formula means in class. This sum is very large (has n ! terms) if n is large, so we will need other ways to compute the determinant, which we will introduce in the next section. The purpose of this formula is to show that there is such a thing as a determinant at all. 1...
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This note was uploaded on 03/31/2012 for the course MA 265 taught by Professor Bens during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Bens
 Linear Algebra, Algebra, Determinant

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