3'3 Systems of Linear Equations and GaussJordan Method

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3.3 Systems of Linear Equations and Gauss-Jordan
Method

• What a generalization of the augmented matrix
  method
• Why means to solve system of any number of
  linear equations or determine that the system is
  inconsistent

2
Idea
Start
a1x1 a2x2 a3x3 d b1x1 b2x2 b3x3 e c1x1
c2x2 c3x3 f
Matrix row operations
Equivalent matrix corresponds to easy to solve
equivalent system Reduced Row-Echelon form
x1 x2 X3
Finish
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Elementary Row Operations

• Switch any two rows
• Multiply or divide one of the rows by a non-zero
  number
• Replace a row by its sum or difference with a
  non-zero multiple of another row

Keep a record of operations
Important
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Reduced Row-Echelon form

• All zero rows are below every non-zero row
• The first non-zero element of every non-zero row
  is 1 (leftmost 1 or leading 1)
• Every leftmost 1 is the only non-zero element
  of its column
• Each leftmost 1 appears to the right of the
  leftmost 1s in the rows above

5
Order of Steps
50, p. 202
If possible
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Applications

• 66, p. 204
• 70, p.204

Hint Re-read the question of the problem to
identify the variables Organize the information
use table or diagram or