A transformation matrix is a mathematical tool used in linear algebra to perform operations on geometric objects, such as points, lines, and shapes. It allows for the manipulation of these objects through various transformations, including translation, rotation, scaling, and shearing. By applying a transformation matrix to a set of coordinates, one can easily change the position or size of the object in a coordinate system. In computer graphics, transformation matrices are essential for rendering images and animations. They enable the efficient calculation of how objects should appear on the screen by transforming their coordinates based on user input or predefined parameters. This process is crucial for creating realistic scenes in video games and simulations, where objects need to move and interact in a dynamic environment.