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Unformatted text preview: . 1/ i C j a i;j det .A i;j /: Since the matrices B j are identical with A except in the i th row, and the sum of the i th rows of the B j s is the i th row of A , we have det .A/ D X j det .B j / D n X j D 1 . 1/ i C j a i;j det .A i;j /: This proves (a). For (b), let B be the matrix that is identical to A , except that the i th row is replaced by the k th row of A . Since B has two identical rows, det .B/ D . Because B is the same as A except in the i th row, B i;j D A i;j for all j . Moreover, b i;j D a k;j . Thus, D det .B/ D X j . 1/ i C j b i;j B i;j D X j . 1/ i C j a k;j A i;j :...
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra, Determinant

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