Answer:
Matrices can be used to represent linear transformations such as those that occur when two-dimensional or three-dimensional objects on a computer screen are moved, rotated, scaled (resized) or undergo some kind of deformation. Each transformation is represented by a single matrix. Matrices are particularly useful for representing transformations in the field of computer graphics, because each transformation can be represented in a consistent format that is easily represented as a computer data structure. In addition, the transformation represented by a matrix M can be undone by applying the inverse of the matrix. In other words, matrix M -1 reverses the transformation applied by matrix M. We will be looking here at some basic examples of using matrices to represent different kinds of transformations of two-dimensional objects. Let's start with simple reflection.Imagine a single point A that has the co-ordinates x = 3, y = 4 relative to the origin (0, 0).Supposing we wish to find the matrix that represents the reflection of any point (x, y) in the x-axis. The transformation involved here is one in which the coordinates of point (x, y) will be transformed from (x, y) to (x, -y). For this to happen, x does not change, but y must be negated. We can therefore achieve the required transformation by multiplying y by minus one (-1). Because we are dealing with a two-dimensional image, all points in the two-dimensional plane are represented by two variables (x and y). The transformations we apply to a point must set values for x and y independently. We will therefore represent our transformation using the two-by-two matrix M:
M = a b
c d
The original position of point A relative to the origin is given by a position vector (x, y) which we can represent using a one-by-two column matrix which we'll call matrix V. By convention, the point created by a transformation is called the image of the original point, and is often given the same label but with the addition of a tick mark (a single apostrophe). Thus A will become A'. The position of point A' relative to the origin after the transformation has been applied is given by the position vector (x, -y), which we can represent using a second one-by-two column matrix which we'll call matrix V '. We can find V ' as follows.