1. ## Matrix multiplication problem

Hi,
I'm trying to solve such a problem that says:

A= [a,b;0,1] "2x2 matrix"

Find A^n

I've tried A,A^2,A^3 to get the formula but I couldn't

2. ## Re: Matrix multiplication problem

Hi ahmedzoro10!

What did you get for A^2 and A^3?

3. ## Re: Matrix multiplication problem

Originally Posted by ILikeSerena
Hi ahmedzoro10!

What did you get for A^2 and A^3?
I got a new matrix for each

4. ## Re: Matrix multiplication problem

Originally Posted by ahmedzoro10
I got a new matrix for each

Which new matrices?

5. ## Re: Matrix multiplication problem

A^2= [a^2,ab+b;0,1]
A^3= [a^3,b(a^2+a+1);0,1]
A^4= [a^4,b(a^3+a^2+a+1);0,1]

6. ## Re: Matrix multiplication problem

Right!

I see a clear pattern. Do you?

Hint: multiply b(a^3+a^2+a+1) with (a-1)/(a-1) to find a simpler expression that does not have an infinite number of terms (if n tends to infinity).

7. ## Re: Matrix multiplication problem

Originally Posted by ILikeSerena
Right!

I see a clear pattern. Do you?

Hint: multiply b(a^3+a^2+a+1) with (a-1)/(a-1) to find a simpler expression that does not have an infinite number of terms (if n tends to infinity).
Woow! I got it,Thanks!!

it's [a^n,b((a^n -1)/a-1),0,1],right?

Right!

9. ## Re: Matrix multiplication problem

Originally Posted by ILikeSerena
Right!
Thanks man!

10. ## Re: Matrix multiplication problem

I'm trying to prove that:

A(A+B)^-1 B=B((A+B)^-1 A)= (A^-1 + B^-1)^-1

A,B and A+B are non singular matrices

11. ## Re: Matrix multiplication problem

Originally Posted by ahmedzoro10

I'm trying to prove that:

A(A+B)^-1 B=B((A+B)^-1 A)= (A^-1 + B^-1)^-1

A,B and A+B are non singular matrices
Hmm, since matrix multiplication is associative, $A(A+B)^{-1} B=B((A+B)^{-1} A)$ is not generally true...

12. ## Re: Matrix multiplication problem

Originally Posted by ILikeSerena
Hmm, since matrix multiplication is associative, $A(A+B)^{-1} B=B((A+B)^{-1} A)$ is not generally true...
Oh ok

13. ## Re: Matrix multiplication problem

Originally Posted by ahmedzoro10
Oh ok
It seems your problem statement is a little off.
Is it perhaps incomplete?
Or is there a typo in it?

14. ## Re: Matrix multiplication problem

Originally Posted by ILikeSerena
It seems your problem statement is a little off.
Is it perhaps incomplete?
Or is there a typo in it?
I've already revised it and it seems cool
The second term could be like that B(A+B)^{-1} A (i.e. with no parenthesis)

15. ## Re: Matrix multiplication problem

Originally Posted by ahmedzoro10
I've already revised it and it seems cool
The second term could be like that B(A+B)^{-1} A (i.e. with no parenthesis)
Hmm, as yet I'm not sure of it.

Either way, as you can see here, your equality with the 3rd part does not hold:
WolframAlpha - counter example

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