Lessons on Matrices

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What are matrices?
These lessons on matrices include: what are matrices, operations on matrices, determinants and inverses of matrices, using matrices to solve systems of equations, Gauss-Jordan Method, Row Reducing Method, Matrix Row Transformation, Cramer's Rule and using determinants to find the area of shapes.

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:

Stall A

Stall B

Stall C

Packs of noodles sold




Packs of rice sold




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 Equal Matrices
Types of Matrices Addition and Subtraction of Matrices
Scalar Multiplication of Matrices Multiplying Two Or More Matrices
Identity Matrix Determinant and Inverse of a Matrix
Singular Matrix Using Matrices to Solve a System of Equations or Simultaneous Equations
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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