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#1 2014-04-02 17:36:58

iLloyd054
Member
Registered: 2014-04-01
Posts: 10

Gauss Elimination & Cramer’s rule to solve equestion

(a)   Consider a system of equations below, 
      


   

   

    Apply Gauss Elimination method to determine the values of x1, x2 and x3.
     
(b)    Use Cramer’s rule to solve the following simultaneous equations.
       

   

   

    Express the values of x, y and z in terms of r, s and t.


I have been trying to solve these two questions but I stuck, especially the first one.


How I did (a):


                     
          Row2 - 2Row1
                     
           Row3 - 4Row1


    then i get 


                   

                   

and here is where I stuck. I just learned these two rules yesterday.

Last edited by iLloyd054 (2014-04-02 18:16:04)

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#2 2014-04-02 19:54:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: Gauss Elimination & Cramer’s rule to solve equestion

b) First:

D = - 60 r s t

Dx = - 48 s t

Dy = - 144 r t

Dz = - 228 r s

D / Dx = x = 4 / (5 r)

D / Dy = y = 12 / (5 s)

D / Dz = z = 19 / (5 t)

So x = 4 / (5 r), y = 12 / (5 s), z = 19 / (5 t)



a) Gauss Jordan elimination. Here is one way.

Add (-2 * row1) to row2

Add (-4 * row1) to row3

Divide row2 by -7

Add (7 * row2) to row3

Divide row3 by -8

Add (-13 / 7 * row3) to row2

Add (-5 * row3) to row1

Add (-3 * row2) to row1


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2014-04-02 21:03:56

iLloyd054
Member
Registered: 2014-04-01
Posts: 10

Re: Gauss Elimination & Cramer’s rule to solve equestion

Thanks bobbym, now I learn new concept about gauss elimination. I didin't know that you can divide to get zero, I was holding on (# * row1) to row3 procedure

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#4 2014-04-02 21:07:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: Gauss Elimination & Cramer’s rule to solve equestion

Hi;

Since you can divide any equation by something other than 0 you can also divide a row.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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