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Vectors In Linear Algebra

  1. May 14, 2008 #1
    Hello!
    I have just started studying linear algebra and I got the following question:

    We have:
    [​IMG]

    Expres u as a linear combination of the vectors v and w.







    This is my attempt;
    (By definition a vector is called a linear combination of [tex]v_{1}, v_{2},... v_{k}[/tex] if it can be expressed in form [tex]c_{1}v_{1}, c_{2}v_{2},... c_{k}v_{k}[/tex] )

    So we get: [tex]c_{1} (4,3,2,1) + c_{2} (1,1,1,1) [/tex]

    Is this right? Is this all we were required to show?

    Thanks you.

     
    Last edited: May 14, 2008
  2. jcsd
  3. May 14, 2008 #2

    Hootenanny

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    You would also need to determine the values of the scalar coefficients.
     
    Last edited: May 14, 2008
  4. May 14, 2008 #3
    How do we find the values of the scalar coefficients i.e., [tex]c_{1} , c_{2}[/tex]? Thant's my problem... :confused:

    Thanks.
     
  5. May 14, 2008 #4

    Hootenanny

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    Well, you have two unknowns which must satsify a system of four equations. Solve.
     
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