Solving nonlinear equations using matrix

[sameera]

1. To solve for six unknown variables using six nonlinear equations using matrix form and to prooce it as singular.
Tp1a_d,Tp2a_d,Tp1b_d,Tp2c_d, Tp3b_d,Tp3c_d are known variables
Tp1,Tp2,Tp3, a,b,c are unknown variables.


2. Tp1a_d =Tp1+a*Tp1
Tp1b_d=Tp1+b*Tp1
Tp2a_d=Tp2+a*Tp2
Tp2c_d=Tp2+c*Tp2
Tp3b_d=Tp3+b*Tp3
Tp3c_d=Tp3+c*Tp3


3. can I use differential equations to solve these equations?
But I need to prove that the known variables are dependent on each other by using matrx method.

 

[quantumdude]

That notation is just hideous. Instead I am going to use letters from the beginning of the alphabet (a,b,c,d,e,f) as the known quantities and letters from the end of the alphabet (u,v,w,x,y,z) as the unknowns. Then your system of equations becomes:

a=u+ux
c=u+uy
b=v+vx
d=v+vz
e=w+wy
f=w+wz

I don't see why you would need to use differential equations or matrix methods. You can eliminate u among the first pair of equations, eliminate v among the second pair, and eliminate w among the third. That will give you 3 equations relating x, y, and z. Use those equations to eliminate 2 variables and solve for the third, and you should be home free.

 

[Architeuthis Dux]

Yes, it is possible to solve these nonlinear equations using matrix methods. To do so, you would first need to rewrite the equations in matrix form. This can be done by setting up a matrix with the coefficients of the unknown variables on one side and the known variables on the other side. For example, the first equation can be written as:

[Tp1] = [1+a] * [Tp1a_d]

Similarly, the second equation can be written as:

[Tp1] = [1+b] * [Tp1b_d]

This can be done for all six equations, resulting in a system of equations in matrix form:

[Tp1] = [1+a 0 0 0 0 0] * [Tp1a_d]
[Tp1] = [1+b 0 0 0 0 0] * [Tp1b_d]
[Tp2] = [0 1+a 0 0 0 0] * [Tp2a_d]
[Tp2] = [0 0 0 1+c 0 0] * [Tp2c_d]
[Tp3] = [0 0 1+b 0 0 0] * [Tp3b_d]
[Tp3] = [0 0 0 0 1+c 0] * [Tp3c_d]

To solve this system of equations, you can use methods such as Gaussian elimination or matrix inversion. However, it is important to note that this system of equations may not have a unique solution and could be singular, meaning that the equations are dependent on each other and do not have a unique solution.

As for using differential equations to solve these equations, it may not be necessary as the equations can be solved using matrix methods. However, if you still want to use differential equations, you can set up a system of differential equations based on the given equations and solve them using numerical methods such as Euler's method or Runge-Kutta methods. But again, the resulting solutions may not be unique and could be dependent on each other.

In order to prove that the known variables are dependent on each other, you can use matrix methods to find the determinant of the coefficient matrix. If the determinant is equal to zero, then the system of equations is singular and the known variables are dependent on each other. Otherwise, if the determinant is non-zero, then the system of equations has