Example 3. It is possible that division by zero may occur during forward elimination steps

It is possible that division by zero may occur during forward elimination steps. For example for the set of equations

during the first forward elimination step, the coefficient of x₁ is zero and hence normalization would require division by zero.

Round-off error:

Naïve GaussEliminationMethod is prone to round-off errors. This is true when there are large numbers of equations as errors propagate. Also, if there is subtraction of numbers from each other, it may create large errors. See the example below.

Remember the previous example where we used Naïve GaussEliminationto solve

using six significant digits with chopping in your calculations. Repeat the problem, but now use five significant digits with chopping in your calculations.

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