I have a system of Linear Simultaneous Equations with n variables. I have solved the equations for particular values of co-efficients of variables & R.H.S. values. Now I am maintaining the co-efficients of variables same & just changing the R.H.S. values. So is there a method of computing the solution of this set of equations from the solution of previous set of equations?

In short, $E_1$: $[A][X] = [B]$ Now equations are solved & solution set $[X]$ is computed. $E_2$: $[A][X] = [C]$ Now how do I compute new solution set $[X]$ using previous solution set? If there is a method to do this quickly compared to again solving the equations then it will be very beneficial to me. Thank You.

  • $\begingroup$ If you had found the inverse of A, while calculating X, then you can directly use it in the next case as well. $\endgroup$ – lsp Apr 5 '13 at 10:06
  • $\begingroup$ sorry but I am calculating by matrix reduction method (Gauss-Jordan) which does not require inverse of matrix. $\endgroup$ – Cool_Coder Apr 5 '13 at 10:14

If you are going to solve $A \, x = b$ with Gauss-Jordan, you can directly solve for both right-hand sides instead. That is, you do Gauss-Jordan with $(a \, b)$ (that is the matrix with the two columns $a$ and $b$) on the right-hand side and perform the usual steps.

Btw: Similarly, you could solve for $A \, X = I$, where $I$ is the identity matrix. Then, you end with $X = A^{-1}$.

  • $\begingroup$ oops that was stupid of me to not realise that. Thanks for reminding me :) $\endgroup$ – Cool_Coder Apr 5 '13 at 12:01

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