The textbook discusses 'shear' transformations but these are NOT part of the official syllabus
First, $P=(x,y)$ is written as column matrix $$\begin{bmatrix} x \ y \end{bmatrix}$$
This column matrix is then pre-multiplied by $A$:
$$x \\ y \end{bmatrix} = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} ax+by\\ cx + dy \end{bmatrix}$$ e.g. let $$A = \begin{bmatrix} 1 & -2 \\ 3 & 1 \end{bmatrix}, \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}$$ $\therefore$ It follows point $(2,3)$ is transformed to $(-4,9)$ (Working out to be done by the reader (in other words too lazy)) **Translation is not a linear transformation, because by definition of linear transformation the origin cannot be moved but a translation will move the origin!** ## The very important property In a linear transformation the origin must be fixed. $$
