Linear Algebra - What is the Rank-Nullity Theorem? | Linear Algebra Basics

What is the rank-nullity theorem, and what does it tell us about linear transformations? In this video, we develop an intuitive and geometric understanding of the rank-nullity theorem in linear algebra. Through simple matrix examples and visualisations, you'll see how the dimension of the column space and the dimension of the null space must add up to all input directions of a linear transformation. If you enjoyed this video, check out the full playlist on linear algebra basics: https://www.youtube.com/playlist?list=PLlenrM60CLlM1C6JDdtVBz1LOzIwTSNCm 📌 Timestamps: 0:00 Introduction 0:43 Rank, Kernel, and Dimensions (Visualisation) 1:51 Statement of the Rank-Nullity Theorem 3:38 2x2 Matrix Example 6:38 2x3 Matrix Example 11:43 Summary Correction: 8:08 Should be -3 instead of +3