# Gauss-Jordan Elimination

Enter integers or decimals into the following system of four linear equations in four unknowns. Be sure to leave no blanks. Then press the "Confirm Entries" button to see the corresponding augmented matrix. Then press the button, which now says "Row Reduce". Starting with the left-most column, the program switches rows to make the pivot entry as large as possible as compared with the other entries in the row (to try to minimize roundoff errors). Next, it applies row operations to try to create a leading 1 and then 0's below the leading 1 in the first column. It then repeats the process, moving to the right from one column to the next. After finishing with the right-most coefficient column, it then applies row operations to put 0's above the leading 1's, moving from right to left. The matrix for each step is shown. Finally, the solution to the system is given.

x_1  +   x_2  +   x_3  +   x_4  =

x_1  +   x_2  +   x_3  +   x_4  =

x_1  +   x_2  +   x_3  +   x_4  =

x_1  +   x_2  +   x_3  +   x_4  =