What is matrix representation in mathematics?

Matrix representation in mathematics refers to a rectangular array of numbers organized in rows and columns. This structure is fundamental in various areas of mathematics, particularly in linear algebra, where it is used to represent systems of linear equations, perform transformations, and work with vector spaces. Each element in the matrix can represent a specific value, and the position of each number indicates its relationship to the others in terms of the mathematical operations being performed.

For example, a matrix can be used to solve simultaneous equations by expressing them in a compact form that can be manipulated using matrix operations such as addition, multiplication, and finding inverses. The organization of numbers in rows and columns makes it easier to understand relationships and perform calculations systematically.