Lessons on Matrices

Matrices (singular: matrix, plural: matrices) have many uses in real life. One application would be to use matrices to represent a large amount of data in a concise manner so that we can process the data in various ways more conveniently.

For example, the sales of different types of pre-packed food from 3 stalls during a given period of time could be shown in the form of a table here:

This table can be represented as a matrix:

This matrix could then be added with another that represents the sales for a different period of time to get the total for the two periods of time, etc.

The topics covered in these lessons on matrices are:

Describing Matrices (includes video)

Equal Matrices

Types of Matrices

Addition and Subtraction of Matrices (includes video)

Scalar Multiplication of Matrices (includes video)

Multiplying Two Or More Matrices (includes video)

Identity Matrix (includes video)

Determinant and Inverse of a Matrix (includes video)

Singular Matrix (includes video)

Using Matrices to Solve a System of Equations or Simultaneous Equations (includes video)

Representing Information Using Matrices

Matrices Videos

Introduction to Matrices

Matrix Addition and Subtraction I
Matrix Addition and Subtraction II

Matrix Scalar Multiplication

Matrix Multiplication I
Matrix Multiplication II
Matrix Multiplication III

Identity Matrix

Determinant of a 2x2 Matrix

Determinant of a 3x3 Matrix I
Determinant of a 3x3 Matrix II

Simplifying Determinant

Inverse of 2x2 Matrix I
Inverse of 2x2 Matrix II

Inverse of 3x3 Matrix

Singular Matrix - A Matrix with no Inverse

Solving a 2x2 System of Equations Using a Matrix Inverse I
Solving a 2x2 System of Equations Using a Matrix Inverse II

Solving a 3x3 System of Equations Using a Matrix Inverse
Using Gauss-Jordan to Solve a System of Three Linear Equations

Row Reducing a Matrix to solve a System of Equations
Solving a System of Equations using Matrix Row Transformations

Cramer's Rule

Using Determinant to find the Area of a Parallelogram
Using Determinant to find the Area of a Triangle and a Polygon

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