Stitz-Zeager_College_Algebra_e-book

Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: = det = = = = For a generic 2 × 2 matrix A = 4 −3 2 1 4 det (A11 ) − (−3) det (A12 ) 4 det([1]) + 3 det([2]) 4(1) + 3(2) 10 ab cd we get ab cd det(A) = det = a det (A11 ) − b det (A12 ) = a det ([d]) − b det ([c]) = ad − bc This formula is worth remembering Equation 8.1. For a 2 × 2 matrix, det ab cd = ad − bc 3 1 2 5 we obtain Applying Definition 8.13 to the 3 × 3 matrix A = 0 −1 2 1 4 3 1 2 5 det(A) = det 0 −1 2 1 4 = 3 det (A11 ) − 1 det (A12 ) + 2 det (A13 ) = 3 det −1 5 14 − det 05 24 + 2 det 0 −1 2 1 = 3((−1)(4) − (5)(1)) − ((0)(4) − (5)(2)) + 2((0)(1) − (−1)(2)) = 3(−9) − (−10) + 2(2) = −13 To evaluate the determinant of a 4 × 4 matrix, we would have to evaluate the determinants of four 3 × 3 matrices, each of which involves the finding the determinants of three 2 × 2 matrices. As you can see, our method of evaluating determinants quickly gets out of hand and many of you may be reaching for the calculator. There is some mathematical machinery which can assist us in calculat...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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