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10.4determinants

# 10.4determinants - Section 10.4 Determinants 2 by 2...

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Section 10.4 - Determinants 2 by 2 determinants : If D = a b c d ! " # \$ % is a 2 x 2 matrix, then the determinant of D is det(D) = a b c d = ad ! bc . 3 by 3 determinants : If D = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ! " # # # \$ % is a 3 by 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 11 a 23 a 32 + a 12 a 21 a 33 )

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Calculating the determinant of a 3 by 3 matrix by expanding a row or column: If D = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ! " # # # \$ % is a 3 by 3 matrix, then the determinant of D may be calculated by expanding about row 1 in the matrix: det (D) = a 11 a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 - a 12 a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 + a 13 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 23 a 32 ) ! a 12 ( a 21 a 33 ! a 23 a 31 ) + a 13 ( a 21 a 32 ! a 22 a 31 ) . Also, the determinant may be calculated by expanding
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10.4determinants - Section 10.4 Determinants 2 by 2...

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