Matrices and linear transformations

Let's apply a linear transformation defined by the matrix [math] T=\begin{bmatrix} a&b \\c&d \end{bmatrix}[/math] - Type in the values for [i]a[/i], [i]b[/i], [i]c[/i], [i]d [/i]in the corresponding boxes. You can explore the effects of the transformation when applied to [i]points[/i], [i]lines[/i], [i]circles[/i], [i]functions[/i], and to the [i]square [/i] having unitary side length with a vertex in the origin. The transformed objects are shown in [i]black[/i]; [i]lines [/i]and [i]curves [/i]are [i]dashed[/i]. There are also some [i]pre-defined transformations[/i]: [i]reflections [/i]about axes, [i]shears[/i], [i]homotecies [/i]and [i]rotations[/i]. In order to use shears, homotecies and rotations, you [i]first [/i]need to use the [i]slider [/i]to set the ratio / rotation angle before pushing the button.