This is the root lecture & it forms a base on Matrix Algebra. It covers some important terminologies that needs to be understand before moving further. Lecture outline :

0:00 Definition of Matrix

0:25 Mathematical Representation of a Matrix

2:09 Dimension of a Matrix. It covers explanation of formula using examples

3:25 Definition of types of Matrix with sample examples

9:15 Solved Examples on construction of matrix

12:52 Practice Questions to test your learning

This lecture focus on Equality of two matrices, kinds of operations applicable on a matrix and properties associated with it. Lecture overview :

0:00 Condition for Equality of matrices

1.29 Solved example to test equality of two matrix

5:42 Definition, condition & solved sample problems on Addition of two or more matrix

9:20 Properties of Matrix Addition

12:05 Definition, condition & solved sample problems on Subtraction of two or more matrix

This lecture explains Matrix multiplication which is one of the important and frequently used tool under Matrix Algebra. Lecture starts with :

0:00 Definition & condition to multiply two or more matrices

2:38 Properties on Matrix Multiplication

3:55 Solved numerical on Matrix product

This lecture describes change of rows into columns & vice-a-verse through transpose. Lecture synopsis :

0:00 Definition of Transpose with mathematical representation & example

2:00 Properties of Transpose

2:34 Verification of properties using solved examples

This lecture is dedicated on a technique to solve determinant of various orders. Lecture summary :

0:00 Definition of Determinant

0:32 Notation & representation

1:50 Determinant of a square matrix having order 1

2.15 Formula to solve determinant of a square matrix of order 2

3:20 Sample problems on 2nd order determinant

6:13 Minor and Cofactor

13:00 Formula to evaluate determinant value of a 3rd order square matrix

17:22 Illustrations on 3rd order determinant

This lecture explains how to find adjoint of a matrix using minor & cofactor. Lecture begins with :

0:00 Definition of Adjoint, notation & mathematical representation

2:02 Solved exercise on Adjoint

This lecture emphasizes on method to evaluate inverse of a matrix using minor, cofactor & adjoint. Lecture overview :

0:00 Definition of Inverse of Matrix

0:48 Formula to find Inverse

1:30 Properties of Inverse

2:46 Illustration

This lecture is based on practical application of Matrix Algebra. One of the application is solving linear equation using matrix. It uses all the fundamentals and concepts that we have learned from the beginning of section 1 to section 4. Lecture synopsis :

0:00 Matrix form of linear equation

2:35 Homogenous & Non-homogenous system of linear equation

4:00 Methods to solve linear equation

4:25 Formula to Solve simultaneous linear equation using inverse of a matrix

6:50 Illustrations

This lecture covers alternative method to solve simultaneous linear equation using row operations. Lecture outline:

0:00 Kinds of row operations

2:45 what is Augmented matrix?

3:32 Sample problems to solve simultaneous equation using row operations

Another method to solve simultaneous linear equation

Quick review and summary of overall course