Explore the fundamental concepts of sums, direct sums, and Gaussian elimination in this comprehensive 45-minute lecture. Delve into the mathematical principles behind these essential topics, gaining a solid understanding of their applications in linear algebra. Learn how to perform calculations involving sums and direct sums, and master the Gaussian elimination method for solving systems of linear equations. Enhance your problem-solving skills and deepen your knowledge of linear algebra through clear explanations and practical examples provided by experts from NPTEL-NOC IITM.