What is Gauss-Jordan elimination?

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Answer 1 · 2014-10-30T01:31:10

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

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.