Gauss Elimination & Cramers rule to solve equestion

iLloyd054 · 2014-04-02 17:36:58

(a) Consider a system of equations below,

Apply Gauss Elimination method to determine the values of x1, x2 and x3.

(b) Use Cramers 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)

bobbym · 2014-04-02 19:54:38

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

iLloyd054 · 2014-04-02 21:03:56

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

bobbym · 2014-04-02 21:07:33

Hi;

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

Math Is Fun Forum

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