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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
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,921

### 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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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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
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,921

### 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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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