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Lecture 4

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

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University of Guelph

Engineering

ENGG 1500

Medhat Moussa

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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