Lect2 - Chapter 1 Matrices and Systems of Equations...

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Unformatted text preview: Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Elementary Row Operations - Example Example . Solve      x 1 + 2 x 2 + x 3 = 3 3 x 1- x 2- 3 x 3 =- 1 2 x 1 + 3 x 2 + x 3 = 4 Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Elementary Row Operations - Example Example . Solve      x 1 + 2 x 2 + x 3 = 3 3 x 1- x 2- 3 x 3 =- 1 2 x 1 + 3 x 2 + x 3 = 4 Solution . The augmented matrix is       1 2 1 3 3- 1- 3- 1 2 3 1 4       Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Elementary Row Operations - Example Example . Solve      x 1 + 2 x 2 + x 3 = 3 3 x 1- x 2- 3 x 3 =- 1 2 x 1 + 3 x 2 + x 3 = 4 Solution . The augmented matrix is       1 2 1 3 3- 1- 3- 1 2 3 1 4       Apply the operations:- 3 R 1 + R 2 , Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Elementary Row Operations - Example Example . Solve      x 1 + 2 x 2 + x 3 = 3 3 x 1- x 2- 3 x 3 =- 1 2 x 1 + 3 x 2 + x 3 = 4 Solution . The augmented matrix is       1 2 1 3 3- 1- 3- 1 2 3 1 4       Apply the operations:- 3 R 1 + R 2 ,- 2 R 1 + R 3 , Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Elementary Row Operations - Example Example . Solve      x 1 + 2 x 2 + x 3 = 3 3 x 1- x 2- 3 x 3 =- 1 2 x 1 + 3 x 2 + x 3 = 4 Solution . The augmented matrix is       1 2 1 3 3- 1- 3- 1 2 3 1 4       Apply the operations:- 3 R 1 + R 2 ,- 2 R 1 + R 3 ,- 1 7 R 2 + R 3 , Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Elementary Row Operations - Example Example . Solve      x 1 + 2 x 2 + x 3 = 3 3 x 1- x 2- 3 x 3 =- 1 2 x 1 + 3 x 2 + x 3 = 4 Solution . The augmented matrix is       1 2 1 3 3- 1- 3- 1 2 3 1 4       Apply the operations:- 3 R 1 + R 2 ,- 2 R 1 + R 3 ,- 1 7 R 2 + R 3 , the augmented matrix becomes       1 2 1 3- 7- 6- 10- 1 7- 4 7       Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Elementary Row Operations - Example Example . Solve      x 1 + 2 x 2 + x 3 = 3 3 x 1- x 2- 3 x 3 =- 1 2 x 1 + 3 x 2 + x 3 = 4 Solution . The augmented matrix is       1 2 1 3 3- 1- 3- 1 2 3 1 4       Apply the operations:- 3 R 1 + R 2 ,- 2 R 1 + R 3 ,- 1 7 R 2 + R 3 , the augmented matrix becomes       1 2 1 3- 7- 6- 10- 1 7- 4 7       We can read the solution from it Chapter 1. Matrices and Systems of EquationsChapter 1....
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This note was uploaded on 04/30/2010 for the course MATH 1111 taught by Professor Dr,li during the Spring '10 term at HKU.

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Lect2 - Chapter 1 Matrices and Systems of Equations...

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