Solution. Working in the matrixform

Working in the matrixform

=

Forward Elimination of Unknowns

Dividing Row 1 by 10 and multiplying by –3, that is, multiplying Row 1 by -0.3, and subtract it from Row 2 would eliminate a₂₁,

=

Again dividing Row 1 by 10 and multiplying by 5, that is, multiplying Row 1 by 0.5, and subtract it from Row 3 would eliminate a_31,

₌

This is the end of the first step of forward elimination.

Now for the second step of forward elimination, we would use Row 2 as the pivot equation and eliminate Row 3 – Column 2_. Dividing Row 2 by –0.001 and multiplying by 2.5, that is multiplying Row 2 by –2500, and subtracting from Row 3 gives

=

This is the end of the forward elimination steps.

Back substitution

We can now solve the above equations by back substitution. From the third equation,

Substituting the value of x₃ in the second equation

Substituting the value of x₃ and x₂ in the first equation,

Hence the solution is

Are there any pitfalls of Naïve GaussEliminationMethod?

Yes, there are two pitfalls of Naïve GaussEliminationmethod.

Division by zero:

Дата добавления: 2014-12-27