# 9/2/2008

## Generalization: Two lines in general

Possible solutions

## General linear Equation

Possible solutions

## Gauss-Jordan Elimination

A method to solve systems of linear equations.

Begin by writing the augmented matrix of the system. Place a cursor in the top entry of the first nonzero column of this matrix.

1. If the cursor entry is zero, swap the cursor row with some row below to make the cursor entry nonzero.
2. Divide the cursor row by the cursor entry.
3. Eliminate all other entries in the cursor column, by subtracting suitable multiples of the cursor row from the other rows.
4. Move the cursor one row down and one column to the right. If the new cursor entry and all entries below are zero, move the cursor to the next column (remaining in the same row). Repeat the last step if necessary.

Return to Step 1. The process ends when we run out of rows or columns. Then, the matrix is in reduced row-echelon from (rref).

See P:\data\math\hartlaub\linear algebra\GaussJordanElimination.mw

## In class Exercise

• Section 1.2 ( page 20) - 1