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#1 2012-10-16 01:17:54

Deon588
Member
Registered: 2011-05-02
Posts: 68

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

View Image: elementary matrices.gif

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#2 2012-10-16 01:32:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,048

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2012-10-16 04:17:36

Deon588
Member
Registered: 2011-05-02
Posts: 68

Re: Product of elementary matrices

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

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#4 2012-10-16 04:28:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,048

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#5 2012-10-16 04:29:47

zetafunc.
Guest

Re: Product of elementary matrices

You multiplied the matrices incorrectly

#6 2012-10-16 04:30:11

zetafunc.
Guest

Re: Product of elementary matrices

Never mind, bobbym was faster.

#7 2012-10-16 05:04:49

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,469

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

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#8 2012-10-16 05:12:02

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,469

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

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#9 2012-10-16 23:04:47

Deon588
Member
Registered: 2011-05-02
Posts: 68

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...

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#10 2012-10-16 23:10:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,048

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#11 2012-10-17 00:39:52

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,469

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

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#12 2012-10-17 08:29:03

Deon588
Member
Registered: 2011-05-02
Posts: 68

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

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#13 2012-10-17 09:50:27

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,469

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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