Matrices

Matrices in Linear Algebra

In linear algebra, a matrix is a fundamental tool used to represent and manipulate data, especially in systems involving multiple variables. Matrices are arrays of numbers or functions arranged in rows and columns, and they are used to perform various operations such as:

• Solving systems of linear equations: Matrices can represent a set of equations, making it easier to solve them using techniques like Gaussian elimination or matrix inversion.

• Transformations: Matrices describe linear transformations, such as rotations, scaling, and shearing, in vector spaces. They help map one set of coordinates to another.

• Data representation: In many fields (e.g., computer graphics, physics, machine learning), matrices are used to organize and process large datasets efficiently.

Overall, matrices help simplify and organize complex operations involving vectors and linear equations.