Problem Description:

Given the following system:

Determine the solution vector using the Gauss Elimination Method.

Problem Solution:

The various steps in the Gauss Elimination Method are as follows:

Step 0 -- form augmented matrix

Step 1 -- i = 1 perform partial pivoting

Step 2 -- i = 1 normalize pivot equation

Step 3+4 -- multiply eqn. i = 1 by 6 and subtract from eqn. j = i+1 = 2

Step 3+4 -- multiply eqn. i = 1 by 0 and subtract from eqn. j = i+2 = 3

Step 1 -- i = 2 perform partial pivoting

Step 2 -- i = 2 normalize pivot equation

Step 3+4 -- multiply eqn. i = 2 by 4 and subtract from eqn. j = i+1 = 3

Stop elimination phase since i = 2 = N-1 = 2

Step 5 – evaluate the last element of the vector

Step 6 – evaluate all other elements (in reverse order)

Therefore the final result is

.