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Math Help - Matrix multiplication problem

  1. #1
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    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
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Matrix multiplication problem

    Hi ahmedzoro10!

    What did you get for A^2 and A^3?
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  3. #3
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    Re: Matrix multiplication problem

    Quote Originally Posted by ILikeSerena View Post
    Hi ahmedzoro10!

    What did you get for A^2 and A^3?
    I got a new matrix for each
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  4. #4
    Super Member ILikeSerena's Avatar
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    Re: Matrix multiplication problem

    Quote Originally Posted by ahmedzoro10 View Post
    I got a new matrix for each


    Which new matrices?
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  5. #5
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    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]
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  6. #6
    Super Member ILikeSerena's Avatar
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    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).
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  7. #7
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    Re: Matrix multiplication problem

    Quote Originally Posted by ILikeSerena View Post
    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?
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  8. #8
    Super Member ILikeSerena's Avatar
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    Re: Matrix multiplication problem

    Right!
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  9. #9
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    Re: Matrix multiplication problem

    Quote Originally Posted by ILikeSerena View Post
    Right!
    Thanks man!
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  10. #10
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    Re: Matrix multiplication problem

    another question,please

    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
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  11. #11
    Super Member ILikeSerena's Avatar
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    Re: Matrix multiplication problem

    Quote Originally Posted by ahmedzoro10 View Post
    another question,please

    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...
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  12. #12
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    Re: Matrix multiplication problem

    Quote Originally Posted by ILikeSerena View Post
    Hmm, since matrix multiplication is associative, A(A+B)^{-1} B=B((A+B)^{-1} A) is not generally true...
    Oh ok
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  13. #13
    Super Member ILikeSerena's Avatar
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    Re: Matrix multiplication problem

    Quote Originally Posted by ahmedzoro10 View Post
    Oh ok
    It seems your problem statement is a little off.
    Is it perhaps incomplete?
    Or is there a typo in it?
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  14. #14
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    Re: Matrix multiplication problem

    Quote Originally Posted by ILikeSerena View Post
    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)
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  15. #15
    Super Member ILikeSerena's Avatar
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    Re: Matrix multiplication problem

    Quote Originally Posted by ahmedzoro10 View Post
    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
    Last edited by ILikeSerena; December 30th 2011 at 03:27 PM.
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