Practical work #6.Gauss Elimination Method. Iterative Method for Solution of Simultaneous Linear Equation

Practical work #6. Gauss Elimination Method. Iterative Method for Solution of Simultaneous Linear Equation

Example 1. Solve the following system of equations by Gauss-Elimination method.

Sol. To eliminate x from the second equation of the system 1, we multiply the first equation by and subtract it from the second equation and obtain.

Similarly, to eliminate x from the third equations of the system 1, we multiply the first euqaiton by and subtract it from the third equation and obtain.

Now, the system of equation 1, becomes

Now, to eliminate y from the third equation of the system (2), we multiply the second equation by 7 and subtract it from the third equation of the system (2) and obtain

Thus, the system of equation (2) becomes

Back substitution gives the solution.

PROBLEM SET

1. Apply Gauss-Elimination method to solve the system of equations.

2. Solve the following system of equations using Gauss-Elimination method:

3. What do you understand by ill-conditioned equations? Consider the following system of equations:

Determine, whether given system is ill-conditioned or not.

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