LU Decomposition Explained | Doolittle’s & Crout’s Method with Examples

In this lecture, we explain the LU decomposition method used in numerical methods to solve systems of linear equations efficiently. LU decomposition factorizes a matrix into two matrices, L (lower triangular matrix) and U (upper triangular matrix). In this video, we clearly discuss the working rule of LU decomposition and how to make the decomposition unique using two important approaches: Doolittle’s method and Crout’s method. 📚 Topics covered in this lecture: Introduction to LU Decomposition Factorization of a matrix into L and U matrices Step-by-step working rule Doolittle’s Method with example Crout’s Method with example How LU decomposition becomes unique Solving systems of linear equations using LU decomposition This topic is very important in numerical methods, numerical analysis, linear algebra, and engineering mathematics and is widely used in scientific computing and matrix computations. This lecture is part of the complete Numerical Methods course, designed for BS Mathematics, Engineering, Computer Science, and university students. Watch the full lecture to clearly understand LU factorization with the Doolittle and Crout methods step by step. 📌 Perfect for: • BS Mathematics students • Engineering students • Competitive exam preparation • Numerical Analysis learners Watch till the end for a complete understanding with theory + graphical intuition + practical examples. Subscribe to Learn with Arisha for more detailed lectures on numerical methods and MATLAB tutorials. 🔹More Playlists: ✅ Numerical Methods Quick Concepts | Short Urdu Videos https://youtube.com/playlist?list=PLQN-EgCjaCPE9hGvVPG4LWdyqYCNS-_Z4&si=aOhbAFoR1XanUrlj ✅Numerical Methods – Full Course https://youtube.com/playlist?list=PLQN-EgCjaCPEH08zW7aUvCJR-BfscRZg-&si=9NwkOOWmed6RkDX1 ✅ 3D Plotting in MATLAB | Learn with Arisha https://youtube.com/playlist?list=PLQN-EgCjaCPFKXGCIzLj-QVcvojLfJVWf&si=-JPTqK-Js0T2lfFV ✅ 2D Plotting in MATLAB | Learn with Arisha https://youtube.com/playlist?list=PLQN-EgCjaCPFUtyWcKDpCbPmcYMC8nnQC&si=McpIOs4a8rcub3Gb ✅ Numerical Analysis Complete Course https://youtube.com/playlist?list=PLQN-EgCjaCPGrYf4xZ0BhxXvPgdZ-Y9ks&si=8SB4AG9_G9CqJ_ue ✅MATLAB for Numerical Computation https://youtube.com/playlist?list=PLQN-EgCjaCPEZZQ5t6xzWn7Xxv3042bjG&si=CGwmwKr6-Dt-y4X- 🚀 Boost Your Numerical Computing Skills! This tutorial is perfect for students, engineers, and programmers who want to understand numerical errors in computational mathematics and MATLAB programming. 💡 Want More Tutorials on Numerical Methods? 👉 Subscribe for more computational math & MATLAB lessons! 👉 Hit the Like button if this video helps! 👉 Have questions? Comment below! 🔔 Stay updated with the latest programming & numerical analysis tutorials! #NewtonRaphsonMethod #NumericalMethods #EngineeringMathematics #NumericalAnalysis #RootFindingMethod #NewtonMethod #RateOfConvergence #QuadraticConvergence # Graphical Explanation #SolvedExample #MathLecture #BSMathematics #EngineeringStudents #CompetitiveExamPreparation #LearnWithArisha #NonlinearEquations #IterationMethod #MathematicsTutorial #MathConcepts #mathyoutube #SecantMethod #convergenceofsecantmethod #rateofconveregnceofsecantmethod #RegulaFalsi #FalsePositionMethod #NumericalMethods #NumericalAnalysis #GaussElimination #GaussJordan #NumericalMethods #LinearEquations #MatrixMethod #engineeringmathematics #PivotingStrategies #PartialPivoting #ScaledPartialPivoting #GaussElimination #NumericalMethods #NumericalAnalysis #LinearEquations #MatrixMethod #EngineeringMathematics #LearnWithArisha #LUDecomposition #DoolittleMethod #CroutMethod #NumericalMethods #LinearAlgebra