Explore the concept of PLU-Decomposition in matrix algebra through this 12-minute educational video. Learn why matrices requiring row swaps for row echelon form don't have LU-decompositions and how permuting rows leads to PLU factorization. Discover the process of multiplying by elementary matrices to achieve row swaps and understand how every square matrix has a PLU decomposition. Apply this knowledge to solve systems of linear equations using PLU factorization. Follow along with step-by-step explanations, from finding LU decompositions to implementing PLU factorization and solving linear systems. Gain valuable insights into this important topic in linear algebra, complementing your understanding of LU decompositions and enhancing your problem-solving skills in matrix operations.