What is Gauss-Jordan elimination?

1 Answer
Oct 30, 2014

Gauss-Jordan elimination is a technique for solving a system of linear equations using matrices and three row operations:

  1. Switch rows
  2. Multiply a row by a constant
  3. Add a multiple of a row to another

Let us solve the following system of linear equations.

#{(3x+y=7),(x+2y=-1):}#

by turning the system into the following matrix.

#Rightarrow ((3" "1" "" "7),(1" "2" "-1))#

by switching Row 1 and Row 2,

#Rightarrow((1" "2" "-1),(3" "1" "" "7))#

by multiplying Row 1 by -3 and add it to Row 2,

#Rightarrow((1" "" "2" "-1),(0" "-5" "10))#

by multiplying Row 2 by #-1/5#,

#Rightarrow((1" "2" "-1),(0" "1" "-2))#

by multiplying Row 2 by -2 and add it to Row 1,

#Rightarrow((1" "0" "" "3),(0" "1" "-2))#

by turning back into a system of equations,

#Rightarrow{(x=3),(y=-2):}#,

which is the solution of the original system.


I hope that this was helpful.