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What can I use to solve a general matrix?

  1. Oct 17, 2011 #1
    Hi guys!

    I need to solve a matrix. I have 3 equations, 3 unknowns, straightforward stuff. And I know it's invertible (doing transformations for hamiltonian dynamics, so I know they made it invertible). I know my calculator and a ton of websites can easily solve any matrix with real coefficients, but here they are general variables.

    Does anyone know a good website (or how to do it on the TI-83, or TI-89) that will do this?

    For example, solving something like:

    a*x + b*y = 3
    ba*x + 4b*y = 5, finding x and y as functions of a and b.

    Any good way?

    Thanks!
     
  2. jcsd
  3. Oct 17, 2011 #2

    phyzguy

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    Science Advisor

    This is of the form M.X = S, so the solution is just [tex]M^{-1}.S[/tex] .

    Wolfram alpha (http://www.wolframalpha.com) will solve this easily. The syntax is :

    Inverse[{{a, b}, {a b, 4 b}}].{3,5}//Simplify

    Try it!
     
  4. Oct 18, 2011 #3

    hotvette

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    Homework Helper

    You can solve the example by substitution. Solve the 1st equation for either x or y and substitute the result into the 2nd equation to solve for the other unknown. You'll end up with algebraic expressions for x and y in terms of a and b.
     
  5. Oct 18, 2011 #4

    jasonRF

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    Science Advisor
    Gold Member

    Phyzguy recommended wolfram alpha, which is a great option. Maxima is another option, possibly more clunky but I use it the most for computer algebra and arbitrary precision arithmetic:

    http://maxima.sourceforge.net/

    enjoy,

    jason
     
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