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Vector equation, find sum

  1. Jan 22, 2007 #1

    fsm

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    1. The problem statement, all variables and given/known data
    Find a and b such that v=au + bw, where u=<1, 2> and w=<1, -1>


    2. Relevant equations
    v=au + bw
    v=<2, 1>


    3. The attempt at a solution
    No attempt

    I really don't know where to begin. There is not an example like this in the book.
     
  2. jcsd
  3. Jan 22, 2007 #2

    cristo

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    Well, try writing the equations in this format:
    [tex]\left(\begin{array}{c}2\\1\end{array}\right)=a\left(\begin{array}{c}1\\2\end{array}\right)+b\left(\begin{array}{c}1\\-1\end{array}\right)[/tex]

    Then set up equations for the x (top) component, and the y (bottom) component, and solve for a and b.
     
  4. Jan 22, 2007 #3

    HallsofIvy

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    Your equation says that a<1, 2>+ b< 1, -1>= <2, 1> or
    <a+ b, 2a- b>= <2, 1>. Since two vectors are equal only if corresponding components are equal, you have the two equations a+ b= 2, 2a- b= 1. Solve those for a and b.
     
  5. Jan 22, 2007 #4

    fsm

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    I actually had it set up like that but thought I was doing something wrong. I didn't know what to do next. Thanks for the help!!!
     
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