# Thread: Linear Transformations

1. ## Linear Transformations

let e1 = $
\begin{bmatrix}1 \\ 0 \end{bmatrix}
$
, e2 = $
\begin{bmatrix}0 \\ 1 \end{bmatrix}
$
, y1= $
\begin{bmatrix}2 \\ 5 \end{bmatrix}
$
,y2 = $
\begin{bmatrix}-1 \\ 6 \end{bmatrix}
$

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

find the images of $
\begin{bmatrix}5 \\ -3 \end{bmatrix}
$
and $
\begin{bmatrix}x1 \\ x2\end{bmatrix}
$

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

help!

2. You are given that $
T\left( {\left[ \begin{gathered}
1 \hfill \\
0 \hfill \\
\end{gathered} \right]} \right) = \left[ \begin{gathered}
2 \hfill \\
5 \hfill \\
\end{gathered} \right]\,\& \,T\left( {\left[ \begin{gathered}
0 \hfill \\
1 \hfill \\
\end{gathered} \right]} \right) = \left[ \begin{gathered}
- 1 \hfill \\
6 \hfill \\
\end{gathered} \right]$
.
You know that $\left[ \begin{gathered}
5 \hfill \\
- 3 \hfill \\
\end{gathered} \right] = 5\left[ \begin{gathered}
1 \hfill \\
0 \hfill \\
\end{gathered} \right] - 3\left[ \begin{gathered}
0 \hfill \\
1 \hfill \\
\end{gathered} \right]$

Now apply the linear transformation.

3. Originally Posted by Plato
You are given that $
T\left( {\left[ \begin{gathered}
1 \hfill \\
0 \hfill \\
\end{gathered} \right]} \right) = \left[ \begin{gathered}
2 \hfill \\
5 \hfill \\
\end{gathered} \right]\,\& \,T\left( {\left[ \begin{gathered}
0 \hfill \\
1 \hfill \\
\end{gathered} \right]} \right) = \left[ \begin{gathered}
- 1 \hfill \\
6 \hfill \\
\end{gathered} \right]$
.
You know that $\left[ \begin{gathered}
5 \hfill \\
- 3 \hfill \\
\end{gathered} \right] = 5\left[ \begin{gathered}
1 \hfill \\
0 \hfill \\
\end{gathered} \right] - 3\left[ \begin{gathered}
0 \hfill \\
1 \hfill \\
\end{gathered} \right]$

Now apply the linear transformation.
got it!