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2331_Notes_5o2_fill - Math 2331 Linear Algebra Section 5.2...

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Math 2331 Linear Algebra Section 5.2 Determinants and Cofactors The properties for determinants in the last section are great, but don't really tell us HOW to find the determinant of a matrix if it is bigger than 2x2. This section develops formulas for determinants in several different ways. PIVOT FORMULA - If A is an nxn matrix, we know we can use elimination to factor A in the form PA = LU P is a permutation matrix L is lower triangular with 1's along the main diagonal U is the upper triangular form of A from elimination By the formula for products, det(P)*det(A) = det(L) * det(U) OR- Finding the determinant by reducing to upper triangular is definitely one way to find a determinant and often a good way. But, not the only way! Before I talk about permutations, let's look at row reducing a general 3x3 matrix - 11 12 13 21 22 23 31 32 33 a a a A a a a a a a = Assume the upper left corner is not 0, Multiply row 2 and 3 by the upper left corner entry-
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