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12.3 Determinants

# 12.3 Determinants - 12.3 Systems of Linear Equations...

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12.3 Systems of Linear Equations: Determinants One method for solving systems of linear equations is called Cramer’s Rule and is based on determinants. This method can only be used when the number of equations equals the number of variables. Evaluating 2 × 2 Determinants: If a, b, c, and d are real numbers, then a b D ad bc c d = = - . Evaluate: 1. 3 2 5 8 - 2. 3 5 2 4 - - Solving a system of two equations in two variables: Given the system ax by s cx dy t + = + = , x s b s b t d t d D x a b D D c d = = = and y a s a s D c t c t y a b D D c d = = = , D ≠ 0 If D = 0, Cramer’s Rule cannot be used; the system is either inconsistent of dependent. Solve: 3. 5 3 21 4 7 2 x y x y - = + = - 4. 8 2 3.4 6 3.3 x y x y - = - - = - Evaluating 3 × 3 Determinants: A 3 × 3 determinant is symbolized by 11 13 2 12 21 2 2 31 3 32 3 3 a a a a a a a a a , where the double subscript indicates its row and column; e.g., entry a 32 is in row 3 column 2. The value of a 3 × 3 determinant is defined in terms of 2 × 2 determinants, called minors of the 3 × 3 determinant.

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12.3 Determinants - 12.3 Systems of Linear Equations...

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