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Homework Help: Coordinates and change of base

  1. May 12, 2012 #1
    1. The problem statement, all variables and given/known data

    3. The attempt at a solution

    I don't understand where 2v1 + 3v2
    4v1 - 3v2

    came from.
  2. jcsd
  3. May 12, 2012 #2
    I see that the vectors are raised to T which I'm pretty sure means they're transposed but that still doesn't get me anywhere.
  4. May 13, 2012 #3


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    Gold Member

    Where's Figure 3.29a? You should post the whole example to help us get a clearer picture of the problem.
  5. May 13, 2012 #4


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    Science Advisor

    You are solving the equations
    [tex]x= \begin{bmatrix}11 \\ 7\end{bmatrix}= a\begin{bmatrix}1 \\ 2\end{bmatrix}+ b\begin{bmatrix}3 \\ 1\end{bmatrix}[/tex]
    which is the same as the two equations a+ 3b= 11 and 2a+ b= 7. Can you solve for a and b?
    [tex]y= \begin{bmatrix}-5 \\ 5\end{bmatrix}= c\begin{bmatrix}1 \\ 2\end{bmatrix}+ d\begin{bmatrix}3 \\ 1\end{bmatrix}[/tex]
    which is the same as the two equations c+ 3d= -5 and 2c+ d= 5. Can you solve for a and b?
    Last edited by a moderator: May 13, 2012
  6. May 13, 2012 #5
    ok, thanks, I got it now.
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