Lessons & Resources On Matrices

Matrix Introduction

What is a Matrix?

A matrix is simply a rectangular arrangement of numbers (or other mathematical objects like symbols or expressions) organized into rows and columns. Think of it like a table of numbers.

Rows: The horizontal lines of numbers. Columns: The vertical lines of numbers.

Why are Matrices Important?
Matrices (singular: matrix, plural: matrices) have many uses in real life. They are used in many areas of math, science, and computer science, including:

Solving systems of equations: Matrices provide a compact way to represent and solve multiple equations at once. Computer graphics: Matrices are used to transform objects in 3D space (rotation, scaling, translation). Physics: Matrices are used to represent physical quantities and transformations. Data analysis and machine learning: Matrices are used to store and manipulate large datasets.

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	36	21	43
Packs of rice sold	27	56	35

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.

Introductory Lessons Focusing Mostly On 2×2 Matrices

• Introduction to Matrices

  Describing Matrices
  Equal Matrices
  Types of Matrices

• Matrix Operations

  Matrix Addition & Subtraction
  Scalar Multiplication
  Matrix Multiplication
  Identity Matrix
  Determinant of a Matrix
  Inverse of a Matrix
  Singular Matrix

• Applications of Matrices

  Solving a System of Equations
  Representing Information

More Lessons On Matrices

(include introductory as well as more advanced materials.)

• Add & Subtract Matrices

  Introduction to Matrices
  Matrix Addition & Subtraction
  Matrix Addition & Subtraction I
  Matrix Addition & Subtraction II

• Multiply Matrices

  Matrix Scalar Multiplication
  Matrix Multiplication I
  Matrix Multiplication II
  Matrix Multiplication III

• Determinant of a Matrix

  Identity Matrix
  Determinant of a 2×2 Matrix
  Determinant of a 3×3 Matrix I
  Determinant of a 3×3 Matrix II
  Find Determinant of Matrix using Row Reduction
  Simplifying the Determinant

• Inverse of a Matrix

  Inverse of a 2×2 Matrix
  Inverse of a 3×3 Matrix
  Singular Matrix(a matrix with no inverse) Singular Matrix

• Solve Systems of Equation using Matrix Inverse

  Solving a 2×2 System of Equations Using a Matrix Inverse I
  Solving a 2×2 System of Equations Using a Matrix Inverse II
  Solving a 3×3 System of Equations Using a Matrix Inverse

• Solve Systems of Equation using Row Transformations

  Using Gaussian Elimination to Solve a System of Equations
  Using Gauss-Jordan Method to Solve a System of Equations
  Row Reducing a Matrix to solve a System of Equations
  Solving a System of Equations using Matrix Row Transformations

• Solve Systems of Equation using Cramer's Rule

  Cramer’s Rule

• Find Area using Determinants

  Using Determinants to find the Area of a Parallelogram
  Using Determinants to find the Area of a Triangle
  Using Determinants to find the Area of a Polygon

Matrices Calculator with step-by-step solutions
Introduction to Matrices, Complex Numbers,
Matrices, Systems of Linear Equations,

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