Terry D. Johnson

10.001 Fall 2000

In the problem below, we have order of magnitude differences
between coefficients in the different rows.

Step 0a: Find the entry in the left column with the largest absolute value. This entry is called the pivot.

Step 0b: Perform row interchange (if necessary), so that
the pivot is in the first row.

Step 1: Gaussian Elimination

Step 2: Find new pivot

Step 3: Switch rows (if necessary)

Step 4: Gaussian Elimination

Step 5: Find new pivot

Step 6: Switch rows (if necessary)

Step 7: Gaussian Elimination

Step 8: Back Substitute

-0.2x_{4} = -0.05; **x _{4}
= 4**

100x_{3} + 200x_{4} = 800;
**x _{3} = 0**

x_{2} + 2x_{3} + x_{4} =4;
**x _{2} = 0**

x_{1} + 2x_{2} + x_{3} = 1;
**x _{1} = 1**

Pivoting helps reduce rounding errors; you are less likely to add/subtract with very small number (or very large) numbers.