This is the first session on my course Matrix methods . Here , you will learn various methods to convert a matrix to its echelon form and normal form. Given a matrix A, you will learn how to find non singular matrices P and Q such that PAQ is normal. A useful topic in college maths. The full course includes Guass Elimination method, Gauss Jordan method, Gauss Seidel method and finding the inverse of a matrix using adjoint. You can contact me for further details.

1. Reduction of matrices to
Normal form: Linear Algebra

2.  Here, you will learn some basic matrix terminology.
 You will learn what is the echelon form of a matrix and how to reduce a matrix to
its echelon form.
 You will also learn about the normal form of a matrix
 Given a matrix A, you will understand how to get 2 non singular matrices P and Q
such that PAQ is in the normal form.

3. Introduction to matrices

13. Question 1

17. Question 2

18. 𝑅3 → 𝑅3 − 𝑅2

21. Question 3

22. To convert to the normal form, first perform elementary row operations and convert to
the echelon form. Then perform elementary column operations and convert to the
normal form.

29. Question 4

34.  You have learnt what is the echelon form and normal form of a matrix.
 how to convert a matrix to the echelon form and find its rank.
 How to find 2 non singular matrices P and Q so that PAQ is in the normal form.