Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

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

(a) Consider a system of equations below,

Apply Gauss Elimination method to determine the values of

(b) Use Cramers rule to solve the following simultaneous equations.

Express the values of

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

How I did (a):

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)*

Offline

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

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.**

Offline

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

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

Offline

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

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.**

Offline