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Math Help - i am so lost help me please

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    5

    i am so lost help me please

    a) Let A and B be two 2 x 2 matrices, each of which commutes (multiplicatively) with C =
    [ 0 1]. show that AB = BA
    [ -1 0]

    b) use mathematical induction to show that for all positive integers n,
    [1 x y]^n
    [0 1 x]
    [0 0 1]
    =
    [1 nx ny+(n(n-1)/2)x]
    [0 1 nx]
    [0 0 1]

    i just started taking this class i have no idea where to start =(
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  2. #2
    Super Member
    Joined
    Apr 2009
    Posts
    678
    Thanks
    1
    a) Let A =
    [a b]
    [c d]

    Given AC = CA perform the multiplications (AC and CA) and find out the relation between a,b,c,d for AC = CA to hold true . As BC = CB same relation will hold for elements of B. Under this relation you can show AB = BA

    b) Again all you need to show is

    [1 nx ny+(n(n-1)/2)x]
    [0 1 nx]
    [0 0 1]

    when multiplied by

    [1 x y]
    [0 1 x]
    [0 0 1]

    gives
    [1 mx my+(m(m-1)/2)x]
    [0 1 mx]
    [0 0 1]

    where m=n+1
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