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Definition: Let A = <nowiki>[aij]</nowiki> be an n x n matrix. The '''determinant''' function, denoted by '''det''', is defined by | Definition: Let A = <nowiki>[aij]</nowiki> be an n x n matrix. The '''determinant''' function, denoted by '''det''', is defined by | ||
| − | det(A) = <math>\sum{a1j1 a2j2... anjn}</math> | + | det(A) = <math>\sum{a1j1 a2j2... anjn}</math> |
where the summation is over all permutations j1, j2... jn of the set S = {1, 2, ..., n}. The sign is taken as + or - according to whether the permutation j1, j2, ... jn is even or odd. | where the summation is over all permutations j1, j2... jn of the set S = {1, 2, ..., n}. The sign is taken as + or - according to whether the permutation j1, j2, ... jn is even or odd. | ||
| + | |||
| + | () | ||
| + | |||
| + | == Example (2 x 2 Matrix) == | ||
| + | |||
[[Category:MA265Fall2012Alvarado]] | [[Category:MA265Fall2012Alvarado]] | ||
Revision as of 11:44, 8 December 2012
THE DETERMINANT
Definition
Definition: Let A = [aij] be an n x n matrix. The determinant function, denoted by det, is defined by
det(A) = $ \sum{a1j1 a2j2... anjn} $
where the summation is over all permutations j1, j2... jn of the set S = {1, 2, ..., n}. The sign is taken as + or - according to whether the permutation j1, j2, ... jn is even or odd.
()
