The system cannot be solved uniquely, which is different from saying that it can't be solved.DDH said:
Assuming U,V,W,u,v,w are known, it might be possible. As a first step, the last three equations in A,B,C are linear, so you can get A,B,C, in terms of u,v,w,a,b,c. Substitute the expression for A into the first three equations. You now have polynomial expressions for a,b,c - good luck!Bruno Tolentino said:
A polynomial system of 6 variables is a set of equations with 6 unknown variables, where each equation is a polynomial expression. These equations are used to find the values of the variables that satisfy all of the equations simultaneously.
To solve a polynomial system of 6 variables, you can use methods such as substitution, elimination, or Gaussian elimination. These methods involve manipulating the equations to eliminate variables and ultimately solve for the remaining variables.
The degree of a polynomial system of 6 variables is the highest degree of any polynomial in the system. It is determined by the highest exponent in any term of the polynomial equations. The degree can range from 0 to infinity.
Polynomial systems of 6 variables are important in mathematics because they are used to model real-world problems and phenomena. They are also used in various fields of science, such as physics, engineering, and economics, to analyze and solve complex systems.
Yes, a polynomial system of 6 variables can have more than one solution. In fact, there can be an infinite number of solutions depending on the complexity of the equations and the constraints placed on the variables. It is important to check for all possible solutions when solving a polynomial system.