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#1 2012-10-17 00:17:54

Deon588
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Product of elementary matrices

Hi all.  I think i'm making a mistake somewhere as the matrix I get after multiplying doesn't seem to be invertible and the next question is to find A^-1.  Is this the right way to do this?
Thanks in advance


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#2 2012-10-17 00:32:17

bobbym
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Re: Product of elementary matrices

Hi;

I am getting:



which can be inverted.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2012-10-17 03:17:36

Deon588
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Re: Product of elementary matrices

Hi Bobbym any idea where I made a mistake?
Thanks a lot

#4 2012-10-17 03:28:19

bobbym
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Re: Product of elementary matrices

Hi;

Your mistake is in line 3. Check how you multiplied those matrices.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#5 2012-10-17 03:29:47

zetafunc.
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Re: Product of elementary matrices

You multiplied the matrices incorrectly

#6 2012-10-17 03:30:11

zetafunc.
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Re: Product of elementary matrices

Never mind, bobbym was faster.

#7 2012-10-17 04:04:49

bob bundy
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Re: Product of elementary matrices

hi Deon588

Your inverses are correct, so then you need to do the multiplying.

(AB)C = A(BC) for matrices so you have a choice of which pair you multiply first.  But you must preserve order.

eg if AB = D you then do DC not CD.

I'm going to do these both ways in case I choose the way you didn't (if you see what mean)



or




Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#8 2012-10-17 04:12:02

bob bundy
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Re: Product of elementary matrices

and you should find that inverse A = E3.E2.E1

This would be a good check that you have inv A right and that your multiplying is OK.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#9 2012-10-17 22:04:47

Deon588
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Re: Product of elementary matrices

Hi Bob thanks a lot for all the effort.  I had no idea how to multiply more than 2 matrices so I tried doing all 3 at once...

#10 2012-10-17 22:10:27

bobbym
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Re: Product of elementary matrices

Hi Deon588;

Always break a big problem down into smaller pieces that you know how to do. This top down design is very common in programming. You knew how to do 2 matrices.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11 2012-10-17 23:39:52

bob bundy
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Re: Product of elementary matrices

hi Deon588

I know the rule for multiplying two matrices.  I dareay you could devise a rule for three but it would be hard to remember.  So two at a time is simplest.

You shouldn't assume that matrices can be swopped around like numbers but associativity { (AB)C = A(BC) } does work.

Beware: commutativity doesn't.  { AB ≠ BA }

Did you try my practice suggestion?

and you should find that inverse A = E3.E2.E1

This would be a good check that you have inv A right and that your multiplying is OK.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#12 2012-10-18 07:29:03

Deon588
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Re: Product of elementary matrices

Yes that was also the next question in the exam paper I did, worked out perfectly at the end smile

#13 2012-10-18 08:50:27

bob bundy
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Re: Product of elementary matrices

up

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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