Lect2 - Chapter 1 Matrices and Systems of Equations Math1111 Systems of Linear Equations x1 2x2 x3 = Elementary Row Operations Example 3 Example Solve

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

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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 0 - 7 - 6 - 10 0 0 - 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 0 - 7 - 6 - 10 0 0 - 1 7 - 4 7 We can read the solution from it
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