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Math Help - Linear Transformations

  1. #1
    Member
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    Linear Transformations

    let e1 = <br />
 \begin{bmatrix}1 \\ 0 \end{bmatrix}<br />
, e2 = <br />
 \begin{bmatrix}0 \\ 1 \end{bmatrix}<br />
, y1= <br />
 \begin{bmatrix}2 \\ 5 \end{bmatrix}<br />
,y2 = <br />
 \begin{bmatrix}-1 \\ 6 \end{bmatrix}<br />


    and T: R^2 --> R^2 be a linear transformation that maps e1 into y1 and maps e2 into y2.

    find the images of <br />
 \begin{bmatrix}5 \\ -3 \end{bmatrix}<br />
and <br />
 \begin{bmatrix}x1 \\ x2\end{bmatrix}<br />


    Ive been messing with this for awhile, I simply dont understand what its asking, or what I am supposed to do.

    help!
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  2. #2
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    You are given that <br />
T\left( {\left[ \begin{gathered}<br />
  1 \hfill \\<br />
  0 \hfill \\ <br />
\end{gathered}  \right]} \right) = \left[ \begin{gathered}<br />
  2 \hfill \\<br />
  5 \hfill \\ <br />
\end{gathered}  \right]\,\& \,T\left( {\left[ \begin{gathered}<br />
  0 \hfill \\<br />
  1 \hfill \\ <br />
\end{gathered}  \right]} \right) = \left[ \begin{gathered}<br />
   - 1 \hfill \\<br />
  6 \hfill \\ <br />
\end{gathered}  \right].
    You know that \left[ \begin{gathered}<br />
  5 \hfill \\<br />
   - 3 \hfill \\ <br />
\end{gathered}  \right] = 5\left[ \begin{gathered}<br />
  1 \hfill \\<br />
  0 \hfill \\ <br />
\end{gathered}  \right] - 3\left[ \begin{gathered}<br />
  0 \hfill \\<br />
  1 \hfill \\ <br />
\end{gathered}  \right]
    Now apply the linear transformation.
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  3. #3
    Member
    Joined
    Jan 2008
    Posts
    175
    Quote Originally Posted by Plato View Post
    You are given that <br />
T\left( {\left[ \begin{gathered}<br />
1 \hfill \\<br />
0 \hfill \\ <br />
\end{gathered} \right]} \right) = \left[ \begin{gathered}<br />
2 \hfill \\<br />
5 \hfill \\ <br />
\end{gathered} \right]\,\& \,T\left( {\left[ \begin{gathered}<br />
0 \hfill \\<br />
1 \hfill \\ <br />
\end{gathered} \right]} \right) = \left[ \begin{gathered}<br />
- 1 \hfill \\<br />
6 \hfill \\ <br />
\end{gathered} \right].
    You know that \left[ \begin{gathered}<br />
5 \hfill \\<br />
- 3 \hfill \\ <br />
\end{gathered} \right] = 5\left[ \begin{gathered}<br />
1 \hfill \\<br />
0 \hfill \\ <br />
\end{gathered} \right] - 3\left[ \begin{gathered}<br />
0 \hfill \\<br />
1 \hfill \\ <br />
\end{gathered} \right]
    Now apply the linear transformation.
    got it!
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