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Math Help - linear combination

  1. #1
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    linear combination

    Given v = [2] and w = [2]. Write [1] as a linear combination of v and w.
    1 1 0
    Just started the chapter. Help please???
    I can't do it here. But number belong in the same bracket.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    [1]=(1/2)v+(1/2)w
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  3. #3
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    I did it wrong. It's supposed to be v=[2,1] where in actuality, 1 is at the bottom of 2. and w =[2, 1] where in actuality,1 is at the bottom of 2. Write [1,0] where in actuality, 0 is at the bottom of 1, as a linear combination of v and w. Can you please show the steps?
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    So v=w? strange... anyway...



    Solve:

    t[2,1]+r[2,1]=[1,0]

    (t+r)[2,1]=[1,0]

    2t+2r=1
    t+r=0

    or

    t+r=1/2
    t+r=0

    1/2=0

    impossible! Hence such t and r aren't exist .


    Different way: w=v=[2,1]

    s[2,1]=[1,0]

    2s=1
    s=0

    the same conclusion!
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