Lect3 - 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 Type of Solutions Theorem For a system of linear equations there are exactly three possibilities: Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Reduced Row Echelon Form Question Is row echelon form unique? Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Reduced Row Echelon Form Question Is row echelon form unique? Ans. NO Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Reduced Row Echelon Form Question Is row echelon form unique? Ans. NO Reduced Row Echelon Form (i) The matrix is in row echelon form (ii) The 1st nonzero entry in each row is the only nonzero entry in its column Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Reduced Row Echelon Form Question Is row echelon form unique? Ans. NO Reduced Row Echelon Form (i) The matrix is in row echelon form (ii) The 1st nonzero entry in each row is the only nonzero entry in its column Example .    1 1    ,       1 3 1 2 1 1       ,       1 2 1       Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Gauss-Jordan Elimination Gauss-Jordan Elimination- a process : augmented matrix row operation-------------→ reduced row echelon form Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Homework 4 Reading Leon (7th edition): p.15 - p.19 Leon (8th edition): p.13 - p.17 Homework 4 Leon (7th edition): Chapter 1 Section 2 Qn. 5(i)-(l), 6, 8 , 9 , 10 Leon (8th edition): Section 1.2 Qn. 5(i)-(l), 6, 8 , 9 , 10 Further Reading Leon (7th edition): p.19-25 Leon (8th edition): p.17-23 Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Goal Augmented matrices leads to consider rectangular arrays of numbers - matrices. A =          a 1 1 a 1 2 ··· a 1 n a 2 1 a 2 2 ··· a 2 n . . . . . . . . . . . . a m 1 a m 2 ··· a m n          Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Goal Augmented matrices leads to consider rectangular arrays of numbers - matrices. A =          a 1 1 a 1 2 ··· a 1 n a 2 1 a 2 2 ··· a 2 n . . . . . . . . . . . . a m 1 a m 2 ··· a m n          Goal Introduce arithmetic operations on matrices Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra References Leon (7th edition) Chapter 1. Section 3 (8th edition) Chapter 1. Sections 1.3-1.4 DeFranza Chapter 1. Sections 1.7 Nicholson (1st edition) Chapter 1. Sections 1.1, 1.4.1-1.4.3, 1.5.1-1.5.2 (2nd edition) Chapter 1. Sections 1.1, 1.4.1-1.4.3, 1.5.1-1.5.2 Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Matrices Definition A matrix is a rectangular array of numbers.is a rectangular array of numbers....
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Lect3 - Chapter 1. Matrices and Systems of Equations...

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