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This course would help in developing understanding on Matrix Algebra. It starts with a lecture on Introduction to matrices to build(brush) up fundamentals and then progresses towards discussing intermediate levels topics including Algebra of matrix, Transpose and Determinants of a matrix, Adjoint and Inverse of matrix.
Throughout the course, emphasis is on learning Matrix Algebra using practice problems. Practical applications of theoretical concepts is of paramount importance too. There is a section dedicated in applying Matrix Algebra constructs for solving system of linear equations.
Curriculum for the course is organized into five different sections containing 12 video lectures and around 3 hours of content. Every section is coupled with sample solved examples and practice problems in the form of a Quiz.
This course is continuously monitored and I shall be more than happy in assisting students on Matrix Algebra queries.
Last but certainly not the least - Feedback is much appreciated!!
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This is the introduction lecture on course to let you know what we will learn in this course.
|Section 1: Introduction to Matrices|
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
|Section 2: Algebra of Matrices|
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
|Quiz 1||4 questions|
Answer to all these questions is 'Solved'
Students are encouraged to solve these practice problems in their notebooks. My purpose would be fulfilled if you can yourself solve and test your answer by using the concepts in the lecture. I have full trust in your ability to solve these questions, reach out to me, if you can't.
|Section 3: Transpose & Determinant|
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
Practice Exercise - 2
|Section 4: Adjoint & Inverse of a Matrix|
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
|Quiz 3||5 questions|
Answers to all these questions is "Solved'
Use the concepts learned in lectures to solve these practice problems in your notebooks. My purpose would be fulfilled if you can yourself solve and test your answer by using the concepts in the lecture. I have full trust in your ability to solve these questions, reach out to me, if you can't.
|Section 5: Application of Matrices in solving a Simultaneous Linear Equation|
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
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
Practice Exercise - 4
|Lecture 11||3 pages|
Another method to solve simultaneous linear equation
|Section 6: Conclusion|
Quick review and summary of overall course
I have taught Mathematics to thousands of students, including students from elementary, secondary and high school as well as college students. For the last 4 years, I have been teaching Mathematics to engineering students.
Teaching is my chosen career path and Mathematics is my passion. After completing my Masters in Mathematics, I have worked at various institutes/schools/colleges as a Coaching Faculty/Teacher/Lecturer.
I believe key to learning mathematics is strong fundamentals and practicing problems in progressive levels of difficulty. I commit myself towards providing such an environment for my students. Till date journey has been positive and rewarding both for me and my students. Hope the saga continues on Udemy too...