Math Is Fun Forum

betahaus

Guest

solving 5 simultaneous equations with matrices

just out of interest, I want to know how to solve the puzzle:

ab = 1
bc = 2
cd = 3
de = 4
ea = 6

Find a,b,c,d,e. It's easy to do normally but I want to know if you can do it using matrices. thanks

also: how do i solve quadratic equations using matrices? like anything in the form ax^2 + bx + c. cheers

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: solving 5 simultaneous equations with matrices

Hi betahaus;

If you mean something like this:

http://www.mathisfunforum.com/viewtopic … 26#p127726

Then the answer is no. There is no analagous technique for non linear equations as there are for linear ones. The only method is newtons iteration done with the Jacobian matrix. That is the only one I have ever seen that uses matrices.

how do i solve quadratic equations using matrices? like anything in the form ax^2 + bx + c.

If you mean determining a,b,c then I have shown you how to do that using matrices in the above link.

Are you sure that the set of non linear equations you have posted are easily solved by normal means?

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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.

Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Re: solving 5 simultaneous equations with matrices

It looks like it can easily be solved by normal means. We are given;

ab = 1
bc = 2
cd = 3
de = 4
ea = 6

Multiply the five equations together;

a²b²c²d²e² = 144

=> abcde = 12

=> cde = 12

=> e = 4

Then just substitute back into ea, and then the rest. That looks like the simplest way to do it - I don't see why one would choose any other method, especially with matrices.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: solving 5 simultaneous equations with matrices

Sweet Devantæ!! Quite clever!
Now I'll do the more evident part
of finding the other four letters.
ea = 6 and e = 4, so a = 1.5
ab = 1 and a = 1.5, so b = 2/3
bc = 2 and b = 2/3, so c = 3
cd = 3 and c = 3, so d = 1
and de = 4, that's 1 times 4.

Last edited by John E. Franklin (2010-01-26 04:35:17)

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igloo myrtilles fourmis

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: solving 5 simultaneous equations with matrices

And remember:

a = -3/2, b = - 2/3, c= -3, d= - 1, e = -4 is also a solution.

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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.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: solving 5 simultaneous equations with matrices

Wow! Bobby! That never crossed my mind!
I was just following from Devant€.  Cool!

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igloo myrtilles fourmis

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: solving 5 simultaneous equations with matrices

I had this scribbled down before I realised that there were more than 2 posts.

ab/bc = a/c = 1/2
a/c x cd = ad = 3/2
ad/de = a/e = 3/8
a/e x ea = a² = 18/8 = 9/4
a = √(9/4) = ± 3/2.

So there are plenty of ways to work it out.

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Why did the vector cross the road?
It wanted to be normal.