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Unformatted text preview: Section 10.4 Determinants Determinants are important mathematical tools that can frequently be used to analyze and solve linear systems. There are various methods for finding determinants. Some of the simpler methods only apply to 2 x 2 and 3 x 3 matrices. Determinants of 2 x 2 matrices If D = a b c d is a 2 by 2 matrix, then the determinant of D is det ( D ) = a b c d = ad bc Example. Find the determinant of D = 1 1 2 3 Solution. 1 1 2 3 = (1)( 3) ( 1)(2) = 1 Determinants of 3 x 3 matrices If D = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 is a 3 x 3 matrix, then the determinant of D is det ( D ) = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 = a 11 a 22 a 33 + a 12 a 23 a 31 + a 13 a 21 a 32 ( a 13 a 22 a 31 + a 12 a 21 a 33 + a 11 a 23 a 32 ) The following is a good device for remembering how to evaluate 3 x 3 determinants. Example. Find the determinant of D = 1 1 2 1 1 1 2 1 Solution. 1 1 2 1 1 1 2 1 = (1)(1)( 1) + ( 1)(1)( 1) + (0)(2)( 2) ((0)(1)( 1) + ( 1)(2)( 1) + (1)(1)( 2)) 1 = 1 + 1 + 0 (0 + 2 2) = 0 Important note. The methods shown above for 2 x 2 and 3 x 3 determinants does NOT apply to 4 x 4 or higherorder determinants....
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This note was uploaded on 12/11/2011 for the course MAC 1140 taught by Professor Kutter during the Fall '11 term at FSU.
 Fall '11
 Kutter
 Algebra, Determinant, Linear Systems, Matrices

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