Applications of matrices include finding the area of a triangle, finding points, solving linear equations and cryptography of data. A matrix is simply a group of numbers, so its applications in the world of mathematics are widely variable.
The area of a triangle is calculated using a determinant, a type of matrix with three rows and columns representing the x and y coordinates of a triangle. The matrix is evaluated for the area. Collinear points can be found using matrices in the same way. The area, however, will evaluate to zero, which means it is a line rather than a triangle.
Cramer's Rule solves a system of equations using matrices. A coefficient matrix is created from the constants in each equation. Data encryption and decryption, or cryptography, also involves matrices and the conversion of a message into units using a key, which makes the interpretation of the message difficult for outsiders.