What is Gauss-Jordan elimination?
Gauss-Jordan elimination is a technique for solving a system of linear equations using matrices and three row operations:
- Switch rows
- Multiply a row by a constant
- Add a multiple of a row to another
Let us solve the following system of linear equations.
by turning the system into the following matrix.
by switching Row 1 and Row 2,
by multiplying Row 1 by -3 and add it to Row 2,
by multiplying Row 2 by
by multiplying Row 2 by -2 and add it to Row 1,
by turning back into a system of equations,
which is the solution of the original system.
I hope that this was helpful.