## Matrices and Matrix Arithmetic

A matrix is a row-column rectangular arrangement of elements. Although primarily developed in the 1850s to solve systems of linear equations in several variables, Matrix theory has been found to have wide applications in mathematics and many sciences including computer graphics, data bases, economics, statistics, physics, etc. Matrices are also visual aids to understand the geometry of multidimensional spaces. We will see that matrices obey certain properties of ordinary arithmetic for numbers and do not obey other properties.

This module is a preparatory lesson where we will learn matrix arithmetic and as such introduces quite a bit of definitions and notation.

**Learning Objectives:**

- Definition and notation of a matrix and its size.
- Types of Matrices – Row, Column, Rectangular, Square, Upper Triangular, Lower Triangular, Null, Identity Matrices
- Matrix Equality, Matrix Addition, Scalar Multiplication
- Properties of Matrix Addition and Scalar Multiplication
- Matrix multiplication and its properties
- Representing systems of linear equations by matrices