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Lecture 4

# Lecture 4 - Systems of Linear Equations Contd - Jan 17 2013.pdf

15 Pages
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School
University of Guelph
Department
Engineering
Course
ENGG 1500
Professor
Medhat Moussa
Semester
Winter

Description
Lecture 4 Chapter 2: Systems of Linear Equations – Cont’d Consistent Systems and Unique Solutions  Consistent system: Asystem that has at least one solution  Inconsistent system: Asystem that does not have any solutions 2 Reduced Row Echelon Form, Rank, and Homogenous Systems  Gauss-Jordan Elimination: procedure of solving a system of equations by complete elimination where the leading variable in the j th equation has been eliminated from every other equation. 3  Reduced Row Echelon Form (RREF): Matrix said to be in RREF if 1) It is in row echelon form 2) All leading entries are 1, called a leading 1 3) In a column with a leading 1, all the other entries are zeros. 4 Applications (Johnson, Riess, Arnold, Introduction to Linear Algebra, Addison Wesley, Fifth Edition, 2002, pp 39-43)  Flows in Networks  What are networks? 5 Some examples of matrices that are in reduced echelon form: 1 0 0 1 0 ∗ 𝐴 = 0 1 0 A = 0 1 ∗ 0 0 1 0 0 0 1 ∗ 0 0 1 0 𝐴 = 0 0 1 𝐴 = 0 0 1 0 0 0 0 0 0 6 Example 7 Row reduce the augmented form of the following system to REF and use it to determine all solutions of the system: 2x 1 4x +23x – 43 – 11x4= 28 5 -x 1 2x - 2 + 2x3+ 5x =4-13 5 - 3x3+ x +46x = -50 3x – 6x + 10x – 8x – 28x = 61 1 2 3 4 5 7 Rank of a
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