Which of the following statements accurately describe the applications or properties of matrix decomposition techniques? Select all that apply.

Matrix decomposition techniques split a complicated matrix into simpler parts, like breaking a big puzzle into smaller pieces, which lets us solve linear systems, compute inverses, and analyze data more easily. By transforming a matrix into forms such as LU, QR, or singular value decompositions, we can perform matrix operations faster and with better numerical stability. These methods also reveal hidden structure, such as rank or dominant directions, which is useful for dimensionality reduction or noise filtering. For example, using singular value decomposition on a photo’s pixel matrix lets us keep only the largest singular values, compressing the image while preserving most of its visual information. Thus, decomposition helps both in efficient computation and in extracting meaningful patterns from data.