was doing a matrix determinant solving and came across this method of solving it via gaussian elimination. just one question, WHY?
there's the simple method of solving them, why to use complex stuff. ://

  • 3
    It's less messy and easier to reason about. Converting the equations to row echelon form allows you to apply back substitution to identify the fewest possible variables at a time. This in turn reduces the complexity of solving the next echelon of variables and so on and so forth.
  • 2
    Simple for humans is not same as simple for computers, For computer, simplicity means lesser computations, Gaussian Elimination is exactly that, as far as I understand, you don't need to calculate determinant explicitly in it, which is a heavy operation.
  • 2
    Because the Gaussian elimination has O(N³) while the cofactor expansion has O(N!) - which is completely unfeasible for anything beyond homework toy problems.

    Math paper on that topic (PDF): https://math.ryerson.ca/~danziger/...
  • 0
    aah, you all make so much sense. the rant was an unhealthy one, for the computers. :(
  • 2
    Good, now take a hard 180 and use Gauss elimination in every problem from now on until you get fed up from using it and rant about how it sucks ass again. Circle of life 😉.
  • 1
    I'm going through this same bullshit. Feel your pain I guess
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