Linear Algebra Lecture 24 | Rank of a matrix

In this linear algebra lecture, I will discuss the rank of a matrix. Before discussing matrix rank, I will discuss row space and column space of matrix. I will also give ways of solving the basis of these two vector spaces.

⏰Timestamps
0:00 Introduction
0:04 Row and Column Vectors
0:27 Row Space and Column Space
1:03 Row equivalent matrices have the same row space
3:21 Method 1: How to Find a Basis for the Row Space
7:44 Method 1: How to Find a Basis for the Column Space
11:08 Which columns of a matrix in REF are redundant?
11:57 Which columns of a matrix not in REF are redundant?
14:58 Theorem on how to get a basis for the column space for a matrix
15:33 Two Bases for the Column Space
17:20 Two Bases for the Row Space
19:42 Row space and Column Space have the same dimension
19:52 Definition of Rank of a Matrix

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