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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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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