Null Space (Kernel) and Range (Image) of a Linear Transformation | Linear Algebra Explained

Welcome to our latest video on Linear Algebra! In this tutorial, we explore two essential concepts: the Null Space (or Kernel) and the Range (or Image) of a linear transformation. Understanding these spaces is crucial for analyzing how transformations affect vector spaces and can help us determine important properties like injectivity and surjectivity.

📌 Topics Covered:
Definition of Null Space (Kernel) and how to find it
Understanding the Range (Image) of a transformation
Step-by-step examples of calculating the null space and range
Applications of null space and range in solving systems of linear equations
Insights into the rank-nullity theorem and its significance
By the end of this video, you’ll have a solid grasp of how to determine the kernel and image of a transformation and understand their significance in the broader context of linear algebra.

👉 Don’t forget to check out our other videos in this series for more foundational concepts!

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By Mexams