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Math Help - matrix powers ... plz help me!!

  1. #1
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    Red face matrix powers ... plz help me!!

    X = [1 1]
    ......[1 1]

    Y = [1 -1]
    .....[-1 1]

    Let A = aX and B= bY, where a and b are constants.

    Use different values of a and b to calculate A^2, A^3, A^4 ...., B^2, B^3...
    By consedering integer powers of A and B, find expression for A^n, B^n , (A+B)^n

    Please help me to figure out this problem!! thanks in advance..
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  2. #2
    Member
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    Hello,

    X^2=2X, X^3=(2X)X=2^2X^2,...
    Y^2=2E, Y^3=(2E)Y=2Y,...

    Now, A^n=(aX)^n=a^nX^n.
    For (A+B)^n, compute them for n=2,3,4,... to see what is going on or just use the binomial theorem.

    Bye.
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  3. #3
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    Quote Originally Posted by wisterville View Post
    Hello,

    X^2=2X, X^3=(2X)X=2^2X^2,...
    Y^2=2E, Y^3=(2E)Y=2Y,...

    Now, A^n=(aX)^n=
    .
    For (A+B)^n, compute them for n=2,3,4,... to see what is going on or just use the binomial theorem.

    Bye.
    Thanks,
    but u wrote, 2^2X^2 , does this means 2^4X ??
    can u please show one example?? thanks
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  4. #4
    Member
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    Aug 2008
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    Hello,

    Sorry, I made a mistake...
    X^2=2X,
    X^3=(X^2)X=(2X)X=2(X^2)=2(2X)=2^2X=4X,
    X^4=(X^3)X=(2^2X)X=2^2(X^2)=2^2(2X)=2^3X=8X,
    X^5=(X^4)X=(2^3X)X=2^3(X^2)=2^3(2X)=2^4X=16X,...
    To summarize, X^n=2^{n-1}X.

    Bye.
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