Algebra 2 4.3 notes

# 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 ² e cx ± dy ² f is ±² . ab cd Your Notes THE DETERMINANT OF A MATRIX Determinant of a 2 ± 2 matrix det ²  ² ad ³ cb Determinant of a 3 ± 3 matrix det ² ² ( aei ± bfg ± cdh ) ³ ( gec ± hfa ± idb ) de gh abc def ghi 82 Algebra 2 Notetaking Guide • Chapter 4

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The area of the triangle shown is: Area ±²³ 1 2 ³  1 2 ³ ± (0 ´ 9 ´ 0) µ (0 ´ ( µ 2) ´ 0) ² ± ³ 1 2 1 ³ µ 13 1 00 1 32 1 µ 1 µ 3 µ 1 x y (0, 0) ( µ 1, 3) (3, 2) Example 2 The Area of a Triangle Your Notes Evaluate the determinant of (a) ±² and (b) . a. ± 5( 4 ) µ 2( µ 3 ) ± 20 ´ 6 ± 26 b. ± ( 2 ´ 0 ´ 8 ) µ ( ´ ´ 0 ) ± 10 µ 0 ± 10 µ 20 4 µ 1 02 µ 201 4 µ 1 0 021 5 µ 3 24
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Algebra 2 4.3 notes - 4.3 Determinants and Cramers Rule...

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