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Algebra 2 4.3 notes - 4.3 Determinants and Cramers Rule...

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Determinants and Cramer’s Rule Goals p Evaluate determinants. p Use Cramer’s Rule. 4.3 VOCABULARY Determinant A real number associated with any square matrix A , denoted by det A or by A Cramer’s rule A method for solving a system of linear equations which uses determinants of matrices Coefficient matrix The coefficient matrix of the linear system ax by e cx dy f is . a b c d Your Notes THE DETERMINANT OF A MATRIX Determinant of a 2 2 matrix det ad cb Determinant of a 3 3 matrix det ( aei bfg cdh ) ( gec hfa idb ) a b d e g h a b c d e f g h i a b c d e f g h i a b c d a b c d 82 Algebra 2 Notetaking Guide Chapter 4
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The area of the triangle shown is: Area 1 2 1 2 (0 9 0) (0 ( 2) 0) 1 2 1 1 3 1 0 0 1 3 2 1 1 3 1 3 1 x y (0, 0) ( 1, 3) (3, 2) Example 2 The Area of a Triangle Your Notes Evaluate the determinant of (a) and (b) . a. 5( 4 ) 2( 3 ) 20 6 26 b. ( 2 0 8 ) ( 0 0 0 ) 10 0 10 2 0 4 1 0 2 2 0 1 4 1 0 0 2 1 5 3 2 4 2 0 1 4 1 0 0 2 1 5 3 2 4 Example 1 Evaluating Determinants AREA OF A TRIANGLE
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