Question

What is Gauss-Jordan elimination?

Answer 1

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.

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I hope that this was helpful.