The document provides an overview of reducing matrices to normal form in linear algebra, including basic matrix terminology and the concept of echelon form. It explains how to perform elementary row and column operations to achieve normal form, as well as how to identify the rank of a matrix. Essential techniques include finding two non-singular matrices, p and q, such that paq is in normal form.

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.