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Unformatted text preview: with two proportional row (or columns),
then det A = 0.
Apply a row operation to reduce A to a matrix with a row (or
column) of zeros. Outline Determinants of Special Matrices Determinants Via Elementary Row Operations Determinant of an Elementary Matrix The Determinant of an Elementary Matrix Corollary
Let E be an n × n elementary matrix.
1 If E is obtained by interchanging two rows of In , then
det E = −1. 2 If E is obtained by multiplying a row of In by a scalar k
(k = 0), then det E = k. 3 If E is obtained by adding a scalar multiple of one row to
another row of In , then det E = 1....
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