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Possibly silly linear algebra question

  1. May 19, 2014 #1
    This is NOT homework.

    I am trying to solve a generalized circuit ( each node is a 4-component generalization) and matrices are 4x4 tensors.

    And I am trying to write them down -- making common nodes "zero" current, ending up with a matrix as in what's shown in the link:


    Is there a non-algebraic, clean matrix-level way of solving the problem I describe there?

    If the answer is not obvious please let me know. :)
  2. jcsd
  3. May 20, 2014 #2


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    Science Advisor

    We can delete the i:th-equation and the variable xi (corresponding to the matrix obtained from A by deleting row i and column j), obtaining a system with n-1 equations and n-1 unknowns, which can be solved by e.g. Gaussian elimination. This gives us values of all variables except xi, which is assumed to be 0. With these values, yi can now be calculated.
  4. May 20, 2014 #3
    Yes - you are right.

    This was exactly what I was looking for.
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