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Linear algebra ordered basis problem

  1. Oct 2, 2013 #1
    1. The problem statement

    find the β coordinates ([x]β) and γ coordinates ([x]γ) of the vector [tex]x = \begin{pmatrix}-1\\-13\\
    9\\
    \end{pmatrix}
    \in\mathbb R[/tex]

    if [tex]{β= \begin{pmatrix}-1\\4\\
    -2\\
    \end{pmatrix},\begin{pmatrix}3\\-1\\
    -2\\
    \end{pmatrix},\begin{pmatrix}2\\-5\\
    1\\
    \end{pmatrix}}[/tex] and [tex]{γ= \begin{pmatrix}3\\-1\\
    -2\\
    \end{pmatrix},\begin{pmatrix}1\\4\\
    -2\\
    \end{pmatrix},\begin{pmatrix}2\\-5\\
    1\\
    \end{pmatrix}}[/tex]


    3. The attempt at a solution

    i read my notes and as i understood it, an ordered basis is the linear combination that you use to obtain a specific vector in a vector space. im not clear on the beta and gamma coordinates,
    and i cant understand why the β and γ basis includes 3 vectors? im thinking on the lines that x is obtained through a combination between the β coordinates and the given β , but that does not get me anywhere. please someone point me in the right direction! thank you

    edit : ok i understand that β times the β coordinates would give the vector before the transformation, and γ
    times the γ coordinates give the vector after transformation. but what exactly is x then? the vector before transformation or the vector after transformation?
     
    Last edited: Oct 2, 2013
  2. jcsd
  3. Oct 2, 2013 #2
    ok i have finally managed to get an answer for this question but im not sure of it at all, this is what i did

    [β]x(a,b,c,d) = x where (a,b,c,d) is the beta coordinate of x

    and i solved this equation and ended up getting some values for a b c and d which i wrote down as the β coordinates. is this wrong?
     
  4. Oct 6, 2013 #3
    our instructor solved this problem so anyone wanna know the solution just let me know :)
     
  5. Oct 6, 2013 #4
    I would like to know.
     
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