The Gauss is to convert a "Normal" 3 equations with 3 unknowns in one step, in which the 1 st equation has 3 unknowns, the 2 nd has 2 unknowns and the third 1 unknown. This will make it easier from the last equation and climbing up, calculate the value of the 3 unknowns.
To transform the system into one that is staged will combine the equations between them (adding them, subtracting, multiplying by a number, etc.).
Example:
The 1 st equation always left the same, (ensuring that this is the easiest) and the 2 nd and 3 rd equation must cancel the term that carries the x. Once we
nullified the terms fixed x we \u200b\u200blet the 1 st and 2 nd equation and cancel the term carries in the 3 rd equation
From the last equation we get that z = -256/-128 = 2, substituting in B''is
- and + 9.2 = 13 Þ y = 5
and in turn substituting in A''get:
2x + 3.5 - 7.2 = -1
Þ x = -1 Therefore the solution of the system is (-1, 5, 2)
Classification of systems: systems of equations
can be of 3 types:
determined compatible system (DSS): a single solution compatible
indeterminate system (SCI): infinite System
solutions incompatible (SI) has no solution
In the above example we have obtained a SCD but when we get the other two guys? . When to perform Gauss
obtain 0 = K, where K is a number other than 0, we obtain an SI as absurd.
For example:
We leave fixed the 1st equation and try to cancel the x in the 2 nd and 3 rd
We remove and 3 rd equation:
As seen we have obtained a absurdity, because 0 does not equal 12, so that the system has no solution. When to perform Gauss
obtain 0 = 0, ie we set aside some equation, and the resulting system has more unknowns equations that we have a SCI based on one or two parameters (depends on the equations that are canceled).
For example:
left as long as the 1 st equation and try to remove the unknown x of the 2 nd and 3 rd equation.
If we try to cancel and 3 second equation we see that we cancel the 3 rd
equation thus obtain a system with two equations and 3 unknowns (there are more unknowns than equations) so it will have infinite solutions. One would for instance give the value z z = 0 and so we would get that y = -13, x = 19
