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

Posted 9 years ago
 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?
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Posted 9 years ago
 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
Posted 9 years ago
 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
Posted 9 years ago
 Dear Moderator, I would like to know the implementation of the solution of linear systems in Mathematica.....Thanks and Regards, Anand
Posted 9 years ago
 Thank you for the clarification. Did you follow the links we posted above? - they have many examples on solving such systems.