This is why no one ever actually evaluates a determinant by this laborious method.Ī simple way to produce the expansion (**) for the determinant of a 3 by 3 matrix is first to copy the first and second columns and place them after the matrix as follows: ![]() ![]() In applying the definition to evaluate the determinant of a 7 by 7 matrix, for example, the sum (*) would contain more than five thousand terms. Using the notation for these permutations given in Example 1, as well as the evaluation of their signs in Example 3, the sum above becomesĪs you can see, there is quite a bit of work involved in computing a determinant of an n by n matrix directly from definition (*), particularly for large n. ![]() ![]() If n is a positive integer, then a permutation of the set S =, and, therefore, six terms in the sum (*):
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