Solution of a general linear system of equations: 4-term n-equations

Questions
1

I have the following system of equations…

y1 = c11 * x11 + c12 * x12 + c13 * x13 + c14 * x14

y2 = c21 * x21 + c22 * x22 + c23 * x23 + c24 * x24

y3 = c31 * x31 + c32 * x32 + c33 * x33 + c34 * x34

…

…

yn = cn1 * xn1 + cn2 * xn2 + cn3 * xn3 + cn4 * xn4

How to solve for x?

2

Dear Srinivasan Anand,

is this a general math question or you looking for an implemention with Wolfram Technologies. This forum is ONLY about topics related to Wolfram technologies and is NOT a general science forum.

For Wolfram Language see:

For a general math discussion please find an appropriate forum, for example: Mathematics Stack Exchange

3

Dear Moderator,
I would like to know the implementation of the solution of linear systems in Mathematica…

Thanks and Regards,
Anand

4

Thank you for the clarification. Did you follow the links we posted above? - they have many examples on solving such systems.

5

Hi Srinivasan Anand,

are you sure that the system is posted correctly. You seem to suggest that you are interested in a linear system, which yours is. But usually I would think of it as “vector = matrix times vector”. Now the y is a vector, the c seems to be a matrix of coefficients and the x in your case is also a matrix, is it not? It that case the linear system would be:

Solve[{
  y1 == c11*x1 + c12*x2 + c13*x3 + c14*x4, 
  y2 == c21*x1 + c22*x2 + c23*x3 + c24*x4, 
  y3 == c31*x1 + c32*x2 + c33*x3 + c34*x4, 
  y4 == c41*x1 + c42*x2 + c3*x3 + c44*x4}, {x1, x2, x3, x4}]

which gives a solution. In the case that you have posted things look differently. If I read your system correctly, all equations are independent. None of the variables occurs in more than one equation. Also, the x_{nj} will be underdetermined: one equation four variables. That means that you can get this relation:

Solve[yn == cn1*xn1 + cn2*xn2 + cn3*xn3 + cn4*xn4, {xn1, xn2, xn3, xn4}]
(*{{xn4 -> -((cn1 xn1)/cn4) - (cn2 xn2)/cn4 - (cn3 xn3)/cn4 + yn/cn4}}*)

The result is a relationship which allows you to determine one of the components of x based on three others and the coefficients of c.

Perhaps I am missing something here…

Cheers,

Marco