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Homework Help: Constructing bases (worked out, please check !)

  1. May 2, 2012 #1
    http://dl.dropbox.com/u/33103477/Union.png [Broken]

    Omiting zeroes because they add nothing:

    [tex] \begin{bmatrix}
    3 & 1 & 7 & 4\\
    5 & 6 & 7 & 3
    \end{bmatrix}[/tex]

    RREF

    [tex] \begin{bmatrix}
    1 & 0 & \frac{35}{13} & \frac{21}{13}\\
    0 & 1 & \frac{-14}{13}& \frac{-11}{13}
    \end{bmatrix} [/tex]

    Hence the basis is:
    [tex]
    \begin{Bmatrix}
    \frac{-35}{13}\\
    \frac{14}{13}\\
    1\\
    0
    \end{Bmatrix}, \begin{Bmatrix}
    \frac{-21}{13}\\
    \frac{11}{13}\\
    0\\
    1
    \end{Bmatrix}[/tex]


    Similarly,

    [tex] \begin{bmatrix}
    6 & 4 & 3 & 6\\
    4 & -1 & 3 & 7
    \end{bmatrix}
    [/tex]

    RREF

    [tex] \begin{bmatrix}
    1 & 0 & \frac{15}{22} & \frac{17}{11}\\
    0 & 1 & \frac{-3}{11}& \frac{-9}{11}
    \end{bmatrix} [/tex]


    So the basis is:
    [tex] \begin{Bmatrix}
    \frac{-15}{22}\\
    \frac{3}{11}\\
    1\\
    0
    \end{Bmatrix}, \begin{Bmatrix}
    \frac{-17}{11}\\
    \frac{9}{11}\\
    0\\
    1
    \end{Bmatrix} [/tex]

    So now that I have U, W I am unsure on how to proceed with the addition and Union.

    Should I just put both matrices ontop of one another and solve that ?
    You don't need to check my bookwork just guidance on the general direction that I heading would be useful.
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. May 3, 2012 #2
    Any one ?
     
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