What type of transformations can a transformation matrix perform?

A transformation matrix can indeed perform translations, rotations, scalings, and reflections, which makes the chosen answer correct.

Each of these transformations corresponds to a different operation in linear algebra. When representing transformations in a coordinate system, matrices can be used to manipulate vectors through matrix multiplication. For example:

• Rotations change the angle of a vector while preserving its length.
• Scalings modify the length of a vector by stretching or compressing it along a certain axis.
• Reflections flip the vector over a specified line or plane.
• Translations move a vector in space from one position to another. Although translations themselves are not represented directly by a linear transformation since they involve changing the origin, in homogeneous coordinates, they can be represented with a specialized matrix.

This versatility in handling various transformations is a fundamental aspect of linear transformations in vector spaces, making it possible to rotate, reflect, and scale figures in geometry, and manipulate data in applications like computer graphics.

The other options do not encompass the full range of transformations that matrix representations can achieve. While rotations and linear transformations may be part of the matrix capabilities, they do not cover the entire set of linear transformations that can be accomplished. Therefore, the correct answer reflects