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Need your help on BASIS.

  1. Aug 12, 2011 #1
    1. The problem statement, all variables and given/known data

    Let v=5t-2,S={v_1,v_2 }={t+1,t-1} is a basis of P_1 where P_1 is a vector space of all polynomials of degree ≤1. What is [v]s? Let v=5t-2,S={v_1,v_2 }={t+1,t-1} is a basis of P_1 where P_1 is a vector space of all polynomials of degree ≤1. What is [v]s?

    2. The attempt at a solution
    I need your help to provide me the correct way of putting the answers together, like the one in the answer scheme. Thanks in advance!
     
  2. jcsd
  3. Aug 12, 2011 #2

    vela

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    You need to show some attempt at doing the problem yourself before receiving help here.
     
  4. Aug 12, 2011 #3
    v=[5t-2]=a[t+1]+b[t-1]

    (1st) at+bt=5t
    (2nd) a-b=-2
    v=3⁄2 v_1+7⁄2 v_2
    [v]_s=[■(3⁄2@7⁄2)]
    is this correct?
     
  5. Aug 12, 2011 #4

    vela

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    Looks good. I'm not exactly sure what the following notation means, though:
     
  6. Aug 12, 2011 #5
    Last edited: Aug 12, 2011
  7. Aug 12, 2011 #6

    HallsofIvy

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    What about those of us who do not use "Microsoft Word Office"?
     
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