Welcome and Introduction
  • Welcome and Introduction
  • SOLUTIONS of Assignments
Basics of Matrices
  • Matrices and their Significance - 001
  • Matrix Notation - 002
  • Dimension (Order) of a Matrix - 003
  • Quiz 1: Dimensions of a Matrix
  • Addressing Elements of a Matrix - 004
  • Quiz 2: Addressing Elements of a Matrix
  • Solving Linear Systems in 2 Unknowns - 005
  • Quiz 3: Solving Linear Systems in 2 Unknowns
  • Solving Linear Systems in 3 Unknowns - 006
  • Quiz 4: Solving Linear Systems in 3 Unknowns
Basics of Matrices (Continued)
  • IMPORTANT - This section is OPTIONAL
  • Types of Matrices
  • Addition and Subtraction of Matrices
  • Multiplication of Scalars with Matrices
  • Multiplication of two Matrices
  • Inverse and Determinant of a 2x2 Matrix
  • The Formula: Inverse (A) = Adjoint (A) / Determinant (A)
  • * EXAMPLE - Inverse of a 2x2 Matrix
  • Using Matrices to Solve Simultaneous Linear Equations
  • * EXAMPLE - Using Matrices to Solve Simultaneous Linear Equations
  • CHALLENGE QUESTION - Using Matrices to Solve Simultaneous Linear Equations
  • SUMMARY
Matrices and Systems of Linear Equations
  • The Online Matrix Calculator: A FREE Tool
  • Systems of Linear Equations
  • Systems of Linear Equations - Continued
  • Elementary Row Operations
  • Row Echelon Form (REF)
  • Reduced Row Echelon Form (RREF)
  • * ASSIGNMENT 1: Matrices and Linear Equations
Matrix Algebra and Operations
  • Matrix Algebra - Addition and Subtraction
  • Matrix Algebra - Scalar Multiplication
  • Matrix Algebra - Matrix Multiplication
  • Transpose of a Matrix
  • ** ASSIGNMENT 2: Matrix Algebra & Operations
Determinant of a Matrix
  • Determinant of a 2x2 Matrix
  • Determinant of a 3x3 Matrix
  • Finding Determinants Quickly
  • *** ASSIGNMENT 3: Computing Determinants
Inverse of a Matrix
  • Inverse exists only for Square Matrices
  • Singular Matrices
  • Importance of Inverse in solving Linear Systems
  • Inverse of a 2x2 Matrix
  • Inverse of a 3x3 Matrix - The Two Methods
  • Inverse of a 3x3 Matrix - The Co-factor Method
  • Inverse of a 3x3 Matrix - Gauss-Jordan Elimination Method
Properties of Determinants
  • Properties of Determinants - Row Operation 1
  • Properties of Determinants - Row Operation 2
  • Properties of Determinants - Row Operation 3
  • Properties of Determinants - All Row Operations
  • Properties of Determinants - Row Operations Applied
  • Properties of Determinants - Another Property
*** OPTIONAL: Introduction to Vectors
  • Introduction to the Section
  • Scalars and Vectors
  • Geometrical Representation of Vectors
  • Vector Addition and Subtraction
  • Laws of Vector Addition and Head to Tail Rule
  • Unit Vector
  • Components of a Vector in 2D
  • Position Vector
  • 3-D Vectors and Magnitude of a Vector
  • Displacement Vector
  • Finding Midpoint using Vectors
Vector Spaces
  • Introduction to Vector Spaces
  • Euclidean Vector Spaces - Part 1
  • Euclidean Vector Spaces - Part 2
  • Euclidean Vector Spaces - Part 3
  • Definition and Closure Properties
  • Axioms of Vector Spaces
  • Example of Closure Properties
  • Example 1 of Vector Spaces
  • Example 2 of Vector Spaces
Subspace and Nullspace
  • Subspaces - Introduction
  • Subspaces - Example
  • Subspaces - Example 2
  • Subspaces - Example 3
  • Nullspace of a Matrix
  • Nullspace of a Matrix - Example
  • **** ASSIGNMENT 4: Vector Spaces, Subspaces and Null Spaces
Span and Spanning Sets
  • Span of a set of vectors
  • Span of a set of vectors - Example
  • Spanning Set for a Vector Space - Introduction and Examples
  • Spanning Set - Example 3
  • Spanning Set - Example 4
Linear Dependence and Independence
  • Linear Dependence - Introduction
  • Linear Dependence - Definition