AUGMENTED MATRICES, TYPES OF SOLUTIONS

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• AUGMENTED MATRICES, TYPES OF SOLUTIONS
• Reference Croft Davision, Chapter 8, Block 3
• http//www.math.utep.edu/sos/math
• Introduction
• Gaussian Elimination is a systematic way of
  simplifying a system of equations. A matrix,
  called an augmented matrix, which captures all
  the properties of the equations, is used. A
  sequence of elementary row operations on this
  matrix eventually brings it into a form known as
  echelon form. From this, the solution to the
  original equations is easily found.

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Augmented Matrix Consider the system of
equations, it can be represented by an
augmented matrix
this vertical line can be omitted as in your
textbook
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Similarly, the following system of
equations can also be written as an
augmented matrix
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e.g. 1 Write down the augmented matrices for
the followings a. b. c.
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Types of Solutions to System of Linear
Equations When a system of linear equations is
solved, there are 3 possible outcomes
i. a unique solution ii. an infinite number
of solutions iii. no solution
Heres some examples i.
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ii. iii. e.g. 2 Solve the system with the
augmented matrix a.
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b.
Exercise p.442 Q1a, 1b, 1c, 2a, 2b, 2c
p.446 Q1a, 1b, 1f, 1g