Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

Inverse Matrices

Hi guys,

Here's an interesting little question.

Given that

prove that

Since

But I don't really know how to divide or factorise matrices, since multiplication is not commutative, so I don't really understand why its

And not

Last edited by Au101 (2010-12-17 03:31:38)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Inverse Matrices

Hi again

How about:

Consider

What is it equal to?

Then use what you are given to show what

is equal to.

Use this to show

And then to the required result.

Can you fill in the gaps?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Inverse Matrices

Hmmm...that's a really good way of thinking about it.

Since

Therefore, by multiplying both sides by

I'm really not sure what to do here, I can't multiply both sides by

However, can I use the reflexivity of addition to say that

Since

Therefore

Last edited by Au101 (2010-12-17 05:49:59)

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Inverse Matrices

I was wondering what you think of this solution:

Last edited by Au101 (2010-12-17 07:31:08)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Inverse Matrices

hi Au101,

I'm really not sure what to do here, I can't multiply both sides by A

But what you have subsequently done is exactly that and it's fine!  So that answer is correct.

Post 4 is also correct.  I had in my mind that there would be more than one way of doing this; and you've shown this is true, so thanks.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Inverse Matrices

Hmmm, I haven't quite multiplied by A, I didn't find that helpful, so I divided by

, which is of course equivalent

Since

is defined as

Thanks a lot, once again, Bob, your help has been invaluable, I was completely stumped as to what to do and probably would never have spotted that link .

Last edited by Au101 (2010-12-17 09:25:31)