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Zeato
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Hi, thank you for viewing this thread. I have been googling for its definition for quite a while, but have not found any yet. Just wondering if there is a definition of it, in mathematical notations and in words?
An Associated Homogeneous System is a set of equations where each equation has the same number of variables and the same degree of each variable. This means that the system can be solved by eliminating the variables one by one until only one equation with one variable remains.
An Associated Homogeneous System has all equations with a constant term of zero, while a Non-Homogeneous System has at least one equation with a non-zero constant term. This means that an Associated Homogeneous System has only the trivial solution of all variables equaling zero, while a Non-Homogeneous System may have non-trivial solutions.
Associated Homogeneous Systems are important in mathematics because they can be used to solve systems of equations with many variables. They also have applications in linear algebra, differential equations, and other areas of mathematics.
To solve an Associated Homogeneous System, the variables are eliminated one by one until only one equation with one variable remains. This can be done using various methods such as substitution, elimination, or Gaussian elimination.
Yes, an Associated Homogeneous System can have infinite solutions if the system is underdetermined, meaning there are more variables than equations. In this case, there will be free variables that can take on any value, resulting in an infinite number of solutions.