Page 1 DETERMINANTS • A Determinant of a matrix represents a single number. • We obtain this value by multiplying and adding its elements in a special way. Page 2 DETERMINANTS • A Determinant of a matrix represents a single number. • We obtain this value by multiplying and adding its elements in a special way. Determinant of a Matrix of Order One • Determinant of a matrix of order one A=[a 11 ] 1x1 is ?? = a 11 = a 11 Page 3 DETERMINANTS • A Determinant of a matrix represents a single number. • We obtain this value by multiplying and adding its elements in a special way. Determinant of a Matrix of Order One • Determinant of a matrix of order one A=[a 11 ] 1x1 is ?? = a 11 = a 11 Determinant of a Matrix of Order Two • Determinant of a Matrix A= ?? 11 ?? 12 ?? 21 ?? 22 2x2 is ?? = ?? 11 ?? 12 ?? 21 ?? 22 = ?? 11 ?? 22 -?? 12 ?? 21 Page 4 DETERMINANTS • A Determinant of a matrix represents a single number. • We obtain this value by multiplying and adding its elements in a special way. Determinant of a Matrix of Order One • Determinant of a matrix of order one A=[a 11 ] 1x1 is ?? = a 11 = a 11 Determinant of a Matrix of Order Two • Determinant of a Matrix A= ?? 11 ?? 12 ?? 21 ?? 22 2x2 is ?? = ?? 11 ?? 12 ?? 21 ?? 22 = ?? 11 ?? 22 -?? 12 ?? 21 Determinant of a Matrix of Order Three • Determinant of a Matrix A = ?? 11 ?? 12 ?? 13 ?? 21 ?? 22 ?? 23 ?? 31 ?? 32 ?? 33 is (expanding along R 1 ) • ?? = ?? 11 ?? 12 ?? 13 ?? 21 ?? 22 ?? 23 ?? 31 ?? 32 ?? 33 = (-1) 1+1 ?? 11 ?? 22 ?? 23 ?? 32 ?? 33 - (-1) 1+2 ?? 12 ?? 21 ?? 23 ?? 31 ?? 33 + (-1) 1+3 ?? 13 ?? 21 ?? 22 ?? 31 ?? 32 = ?? 11 (?? 22 ?? 33 -?? 32 ?? 23 ) -?? 12 (?? 21 ?? 33 -?? 31 ?? 23 ) + ?? 13 (?? 21 ?? 32 -?? 31 ?? 22 ) = ?? 11 ?? 22 ?? 33 -?? 11 ?? 32 ?? 23 -?? 12 ?? 21 ?? 33 + ?? 12 ?? 31 ?? 23 + ?? 13 ?? 21 ?? 32 -?? 13 ?? 31 ?? 22 Page 5 DETERMINANTS • A Determinant of a matrix represents a single number. • We obtain this value by multiplying and adding its elements in a special way. Determinant of a Matrix of Order One • Determinant of a matrix of order one A=[a 11 ] 1x1 is ?? = a 11 = a 11 Determinant of a Matrix of Order Two • Determinant of a Matrix A= ?? 11 ?? 12 ?? 21 ?? 22 2x2 is ?? = ?? 11 ?? 12 ?? 21 ?? 22 = ?? 11 ?? 22 -?? 12 ?? 21 Determinant of a Matrix of Order Three • Determinant of a Matrix A = ?? 11 ?? 12 ?? 13 ?? 21 ?? 22 ?? 23 ?? 31 ?? 32 ?? 33 is (expanding along R 1 ) • ?? = ?? 11 ?? 12 ?? 13 ?? 21 ?? 22 ?? 23 ?? 31 ?? 32 ?? 33 = (-1) 1+1 ?? 11 ?? 22 ?? 23 ?? 32 ?? 33 - (-1) 1+2 ?? 12 ?? 21 ?? 23 ?? 31 ?? 33 + (-1) 1+3 ?? 13 ?? 21 ?? 22 ?? 31 ?? 32 = ?? 11 (?? 22 ?? 33 -?? 32 ?? 23 ) -?? 12 (?? 21 ?? 33 -?? 31 ?? 23 ) + ?? 13 (?? 21 ?? 32 -?? 31 ?? 22 ) = ?? 11 ?? 22 ?? 33 -?? 11 ?? 32 ?? 23 -?? 12 ?? 21 ?? 33 + ?? 12 ?? 31 ?? 23 + ?? 13 ?? 21 ?? 32 -?? 13 ?? 31 ?? 22 • http://www.authorstream.com/Presentation/j oshsmith1110-162211-determinants-math- ppt-shella-paglinawan-education-powerpoint/Read More

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