Gauss-Jordan Method

Description

The Gauss-Jordan elimination is a method for solving systems of linear equations of $n$ equations and $n$ unknowns:

\begin{matrix} a_{11}x_1 & + & a_{12}x_2 & + & \cdots & + & a_{1n}x_n & = & b_1 \\ a_{21}x_1 & + & a_{22}x_2 & + & \cdots & + & a_{2n}x_n & = & b_2 \\ \vdots & & \vdots & & & & \vdots & = & \vdots \\ a_{n1}x_1 & + & a_{n2}x_2 & + & \cdots & + & a_{nn}x_n & = & b_n \end{matrix}

Represent the system as an augmented matrix
Manipulate the rows until the matrix is in reduced row echelon form:
- Swapping the positions of two rows.
- Multiplying a row by a non-zero scalar.
- Adding to one row a scalar multiple of another.
Each variable now has it’s value

Number of equations

a11 x1

a12 x2

a13 x3

= b1

a21 x1

a22 x2

a23 x3

= b2

a31 x1

a32 x2

a33 x3

= b3