Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By DeMath

Math Help - plz help

  1. #1
    Newbie
    Joined
    Jun 2012
    From
    Pakistan
    Posts
    5

    plz help

    file is attached
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member DeMath's Avatar
    Joined
    Nov 2008
    From
    Moscow
    Posts
    473
    Thanks
    5

    Re: plz help

    Quote Originally Posted by saqifriends View Post
    Let B=\{b_1, b_2\} and C=\{c_1, c_2\} be the bases for \mathbb{R}^2. Find the change-of-coordinates matrix from B to C, and change-of-coordinates matrix from C to B where;

    b_1=\begin{bmatrix}-1\\8\end{bmatrix}\!,\, b_2= \begin{bmatrix}1\\-5\end{bmatrix}\!,\quad c_1=\begin{bmatrix}1\\4\end{bmatrix}\!,\,c_2 = \begin{bmatrix}1 \\ 1 \end{bmatrix}\!.
    If I understand your task, then the solution has the form

    {\begin{gathered}C=BT~~\Rightarrow~~ T={B^{-1}}C={\left[\!\!\begin{array}{*{20}{r}}{-1}&1\\8&{-5}\end{array}\!\!\right]^{-1}} \left[\!\!\begin{array}{*{20}{r}}1&1\\4&1\end{array}\!\!  \right]= \frac{1}{3}\left[\!\!\begin{array}{*{20}{r}}5&1\\8&1\end{array}\!\!  \right] \left[\!\!\begin{array}{*{20}{r}}1&1\\4&1\end{array}\!\!  \right]=\ldots= \left[\!\!\begin{array}{*{20}{r}}3&2\\4&3\end{array}\!\!  \right]\!.\hfill\\[9pt] B=CT~~\Rightarrow~~ T={C^{-1}}B={\left[\!\!\begin{array}{*{20}{r}}1&1\\4&1\end{array}\!\!  \right]^{-1}} \left[\!\!\begin{array}{*{20}{r}}{-1}&1\\8&{-5}\end{array}\!\!\right]= \frac{1}{3}\left[\!\!\begin{array}{*{20}{r}}{-1}&1\\4&{-1}\end{array}\!\!\right] \left[\!\!\begin{array}{*{20}{r}}5&1\\8&1\end{array}\!\!  \right]=\ldots= \left[\!\!\begin{array}{*{20}{r}}3&{-2}\\{-4}&3\end{array}\!\!\right]\!.\hfill\\ \end{gathered}}
    Thanks from saqifriends
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2012
    From
    Pakistan
    Posts
    5

    Re: plz help

    Thank you very much
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum