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Math Help - basis

  1. #1
    krg
    krg is offline
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    basis

    let S = { v1 , v2} T = { w1, w2} be bases for R2

    Given: V1 = ( 1, -2) V2= ( 3, 0)

    Transition matrix from T to S be
    [ 1 2 ]
    [-1 0]


    Find w1 and w2.

    Please help me with the steps. I am not sure where to start!! Thanks!
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  2. #2
    Junior Member
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    The column vectors of your matrix (1,-1) and (2,0) are the coordinates of w1 and w2 on respect to the basis S.
    It means that w_1=1v_1-1v_2 and w_2=2v_1-0v_2
    Which gives
    w_1=(-2,-2)
    w_2=(2,-4)
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