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## #1 2005-09-03 07:54:56

oechel
Member
Registered: 2005-09-01
Posts: 3

### Equations solving

Does somebody have a sollution to solve equations which have more equations then parameters

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## #2 2005-09-03 11:02:50

MathsIsFun
Registered: 2005-01-21
Posts: 7,660

### Re: Equations solving

You should be able to reduce the number of equations, let's try an example:

a+b=2c
a-b=c

That has 3 unknowns but only 2 equations, so let's do our best to solve it:

Combine the two: a+b = 2c = 2(a-b)
Therefore: a+b = 2a - 2b
Subtract a from both sides: b=a-2b
Add 2b to both sides: 3b = a

So we end up reducing this to:

a = 3b

So, we have a range of solutions.

For example: b=1, a=3b=3, a+b=4, a-b=2, c=2
Or: b=2, a=3b=6, a+b=8, a-b=4, c=4
etc ...

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #3 2005-09-03 19:32:58

oechel
Member
Registered: 2005-09-01
Posts: 3

### Re: Equations solving

Thanks, but the problem is more complicated.
Each parameter is a measured value, the result is a rating from 0-10
I'm wondering if there exists a program to solve this kind of matrix

As an example:
12a + 26b - 36c + 44d + 3e = 9
7a + 99b + 255c + 0d - 55e = 3
56a - 44b + 92c + 66d + 22e = 5
2a + 69b + 55c + 37d + 36e = 10
5a + 68b - 44c + 87d + 33e = 1
99a + 51b + 33c + 5d - 48e = 6
...
and so on, totally 20 equations

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## #4 2005-09-03 19:51:04

MathsIsFun
Registered: 2005-01-21
Posts: 7,660

### Re: Equations solving

Oh, got it the wrong way around LOL!

OK, I need to know a little more. Is the data "soft" or "hard" (my words), in other words, is it

A) like a survey where the data is not exact, or
B) is each one an actual equation (ie, if you have values for a to e then they will always get the results shown)

If it is A) then it is Statistics, in other words something like "people who have 12 of a, and 26 of b ... have a satisfaction level of 9". And in Statistics there are many different ways of solving the "best fit", depending on how the data was collected and what results you want.

If it is B), then just pick any 5 and solve them, the rest should also be right

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #5 2005-09-03 21:41:44

oechel
Member
Registered: 2005-09-01
Posts: 3

### Re: Equations solving

The data comes indeed from a survey
Then what kind of statistical analysis method should I use?

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## #6 2005-09-03 22:46:59

MathsIsFun
Registered: 2005-01-21
Posts: 7,660

### Re: Equations solving

Ahhh, good question. I am not a statistics guru, perhaps another member has more knowledge on this than I do.

I can tell you that in practice most people use statistical analysis software for this job. A good program will give you many different ways to analyze the data.

You see, you may want to look at different aspects of the data, for example how each component affects the result (for example "a" and "c" might be very influential) (I seem to recall Analysis of Variance is useful here, look for the term ANOVA or MANOVA)

But if you just want to do a simple job, put the data into Excel and play with it!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #7 2005-09-04 03:57:44

kylekatarn
Member
Registered: 2005-07-24
Posts: 445

### Re: Equations solving

solving 20 equations to 20 variables can be done with something as simple as a Ti84 calculator

just enter the coefs into a matrix and then use the command rref( 'matrix name' ) to get the solution matrix

rref - reduced row echelon form.

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