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Power-User

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Determinant Solution For Linear Simultaneous Eqns.

09/24/2010 3:03 AM

Can any one give proof of the determinant based solution to 'n' nos. linear simultaneous equations ? If not, can anyone give proof of the following which ultimately will give the proof of the solution by induction method.

Determinant [A11...Arr] = Det.[A11...A(r-1)(r-1)] x Det.[A22...Arr] - Det.[A21...Ar(r-1)] x Det.[A12....A(r-1)r]

K.A.Sharma

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Power-User

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#1

Re: Determinant solution for linear simultaneous eqns.

09/24/2010 4:09 AM

Sorry guys,

I am the poser of the question. The Right Hand Side has a common factor of (r-1) power multiplied by the expression. This was missed by me.

K.A.Sharma

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#2

Re: Determinant Solution For Linear Simultaneous Eqns.

09/24/2010 3:34 PM

An advanced algebra book that includes a treatment of solving simultaneous equations using linear algebra would provide the theory. There is no point to someone here simply repeating the proof you can find in a library with a little effort.

Here's a link to some discussion of it:

http://www.akiti.ca/SimEqR12Solver.html

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Power-User

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#3
In reply to #2

Re: Determinant Solution For Linear Simultaneous Eqns.

09/25/2010 4:09 AM

The link gives the procedure to solve - agreed and most people know it. But that's not a proof. The proof should give how the determinant based solution was arrived at for a general 'n' nos. linear equations. I haven't been able to find it anywhere.

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