Matrix Algebra

139 students enrolled

Learn and develop understanding for solving mathematical problems on Matrix Algebra in few steps

139 students enrolled

What Will I Learn?

- By the end of this course, you will be able to develop understanding on how to solve problems on Matrix Algebra.
- This course will enable students in solving problems on Matrix Algebra in their school/college curriculum
- Learn how to apply fundamental Matrix Algebra concepts in solving practical problems

Requirements

- Basic Mathematics

Description

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!!

**"Happy Learning" !!**

Who is the target audience?

- Middle School & High School Students
- 11th & 12th Graders

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Curriculum For This Course

12 Lectures

02:37:38
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What are we going to discuss?
1 Lecture
03:08

This is the introduction lecture on course to let you know what we will learn in this course.

Preview
03:08

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Introduction to Matrices
1 Lecture
13:39

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

Preview
13:39

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Algebra of Matrices
2 Lectures
27:37

This lecture focus on* Equality of two matrices, kinds of operations*

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

Matrix Addition & Subtraction

15:29

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

Matrix Multiplication

12:08

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.

Practice Exercise - 1

4 questions

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Transpose & Determinant
2 Lectures
34:35

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

Transpose of Matrix

11:07

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

Determinant of a Matrix

23:28

Practice Exercise - 2

3 questions

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Adjoint & Inverse of a Matrix
2 Lectures
26:40

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

Adjoint

13:35

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

Inverse of a Matrix

13:05

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.

Practice Exercise - 3

5 questions

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Application of Matrices in solving a Simultaneous Linear Equation
3 Lectures
47:48

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

By using Inverse of matrix

25:30

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

By using Elementary Row Operations

22:18

Practice Exercise - 4

2 questions

Another method to solve simultaneous linear equation

Row Echelon form

3 pages

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Conclusion
1 Lecture
01:11

Quick review and summary of overall course

Wrap up

01:11

About the Instructor