3_7 Cramer's Rule

# 3_7 Cramer's Rule - Cramers Rule Cramers Rule Cramers Rule...

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Cramer’s Rule

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Cramer’s Rule 11 12 21 22 a a A a a Cramer’s Rule for a System of 2 Linear Equations and 2 Unknowns 11 22 12 21 det( ) A a a a a Where matrix A: The system of 2 linear equations in 2 unknowns: 12 2 2 2 1 11 21 a a a b x x y a b y Matrix Form: 12 1 2 1 2 1 21 2 x y b a a a a b has a unique solution if and only if : det( ) 0 A The solutions: 12 2 1 2 2 det det( ) a a x A b b 11 2 21 1 det det( ) b b y A a a
Cramer’s Rule 3 4 2 8 A det( ) 3(8) 4( 2) 32 A Solve the system using Cramer’s Rule: 12 2 2 2 1 11 21 a a a b x x y a b y Matrix Form: 20 8 3 2 4 8 x y   The solutions: 12 2 1 2 2 det det( ) a a x A b b 11 2 21 1 det det( ) b b y A a a 4 8 0 8 3 2 2 x y x y 4 8 et 20 d 2 8 3 20(8) 4( 8) 160 32 192 6 32 32 32 20 8 t 3 de 2 2 3 3( 8) 20( 2) 24 40 16 1 32 32 32 2 1 6, 2

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Cramer’s Rule 11 12 13 21 22 23 31 32 33 a a a A a a a a a a Cramer’s Rule for a System of 3 Linear Equations and 3 Unknowns The system of 3 linear equations in 3 unknowns: 13 2 11 12 22 3 1 21 3 2 1 2 3 3 33 x y z x y z x b b b a a a a a a y z a a a Matrix Form: 11 21 12 2 1 2 13 23 33 2 32 3 31 a a a a a b x a b a b a a y x      has a unique solution if and only if : det( ) 0 A The solutions: 1 2 3 12 22 3 13 23 3 2 3 det det( ) a a a b b x A a a a b

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