Finite Mathematics

Finite Mathematics covers mathematical concepts and techniques applicable to business and social sciences, including matrix algebra, linear programming, and probability.

Basic Concepts

Matrix Algebra

Introduction to Matrix Algebra

Matrices are rectangular arrays of numbers, symbols, or expressions arranged in rows and columns. Matrix algebra is the study of how to add, subtract, and multiply these arrays, as well as how to use them to solve systems of equations.

Matrix Operations

Matrices can be added or subtracted if they are the same size. Multiplying matrices is trickier; you multiply the rows of the first by the columns of the second. The result is useful for modeling complex relationships.

Why Use Matrices?

Matrices are powerful tools in business and science. They help organize data, model networks, and solve problems with lots of variables at once.

Real-World Example

Companies use matrices to track sales in different regions, plan supply chains, and even analyze social connections.

Key Formula

\[C = AB\]

Examples

  • A business tracks product sales across months using a matrix, with products as rows and months as columns.

  • Solving for unknowns in a system like \(2x + 3y = 8\), \(x - y = 2\) can be done with matrices.

In a Nutshell

Matrix algebra organizes and solves complex problems using rows and columns of numbers.

Key Terms

Matrix
A rectangular arrangement of numbers in rows and columns.
Matrix Multiplication
Finding a new matrix by combining rows of one matrix with columns of another.
Determinant
A special number that can be calculated from a square matrix.