CH ENGR 109 Study Guide - Quiz Guide: Lu Decomposition, Pivot Element, Triangular Matrix
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Cbe 109 - numerical and mathematical methods in chemical and biological. Y i=1 a ii where i is the number of row interchanges. In gauss elimination, the matrix a is undergoing a series of elementary transformations as follows: A a1 a2 a3 a . The transformations can be either interchange of rows(columns) or additions of multiples of one row (column) to another row (column). The as are the intermediate matrices during the transformations. From properties 1 and 2, the absolute values of the determinants of these as are equal. Since only an interchange changes the sign of the determinant and there are totally. I times of interchanges, the relationship between the determinants of a and a is det a = ( 1)i det a . The determinant of a is the multiplication of its diagonal elements due to the upper triangular structure: n. Therefore the proof is completed: (10 points) det a = a ii.
