A transformation is a function defined from $$R^2$$\$R^2\$ to $$R^2$$\$R^2\$ that may take any point and translate (move) it to any other point, but in this instance I will only work with Linear Transformations (adapting the program for any transformation is easy though).
A = | a b |
| c d |
$$A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$$
A = |1 -2|
|0.5 2|
$$A= \begin{pmatrix} 1 & -2\\ 0.5 & 2 \end{pmatrix}$$
A = |1 -2 |
|2 -4 |
$$A= \begin{pmatrix} 1 & -2\\ 2 & -4 \end{pmatrix}$$
A = |1 -2 |
|k*1 -2k* |
For any real $$k$$$$A= \begin{pmatrix} 1 & -2\\ k & -2k \end{pmatrix}$$
For any real \$k\$.
A = | 0 0 |
| 0 0 |
$$A= \begin{pmatrix} 0 & 0\\ 0 & 0 \end{pmatrix}$$
