Linear Algebra Full Course: Beginner to Advanced Linear Algebra (14hours Linear Algebra Mastery)
Welcome to your ultimate Linear Algebra Full Course, a complete and immersive Linear Algebra Full Course that makes complex topics straightforward and accessible. Whether you're starting from the basics or seeking a comprehensive review, this Linear Algebra Full Course covers everything, from matrices to vector spaces, inverses to subspaces in just 14 hours. 📌 What You’ll Master: -Solving systems of linear equations with Gaussian elimination and Gauss–Jordan methods -Computing matrix inverses, products, determinants, and transformations -Exploring vector spaces, subspaces, basis, dimension, null space, and column space -Understanding linear independence, rank, and orthogonality with real-world examples -Applying matrix transformations like projection, reflection, rotation, and shear, complete with visual insights and practical applications This Linear Algebra Full Course is designed to combine deep understanding with structured flow, helping you gain both conceptual clarity and procedural fluency. Whether you're self-studying or following an academic path, you're about to master linear algebra in an engaging, efficient way. Each concept is broken down into clearly labeled sections with helpful timestamps, so you can jump directly to what you need just like an interactive textbook. If you're prepared for exams like the GRE, SAT, university midterms, or simply want to build a solid foundation in Linear Algebra, this full course is your go‑to resource. We emphasize clarity, visual examples, and consistent learning checkpoints. 🔔 Want more math content? Subscribe and hit the bell to stay updated with in‑depth Linear Algebra tutorials like this one, covering calculus, probability, and beyond. Chapters: 00:00:00 Intro to linear equations 00:02:38 General form of systems of linear equations 00:04:22 Solutions to linear systems (2 and 3 unknowns) 00:07:38 Worked examples on solutions to linear systems 00:14:49 Augmented matrices 00:17:05 Row operations on augmented matrices 00:24:22 Row echelon forms 00:30:03 Worked examples on row echelon forms 00:34:34 Gauss-Jordan vs Gaussian elimination 00:42:59 Homogeneous linear systems 00:47:08 Gaussian elimination with back substitution 00:51:34 Matrix notation, vectors and size 00:54:17 Basic matrix operations 00:58:20 Matrix multiplication 01:03:50 Partitioned matrices 01:08:52 Matrix products and linear combinations 01:10:59 Matrix transpose 01:13:26 Intro to matrix inverse 01:19:13 Inverse of matrix products 01:21:24 Powers of matrices 01:24:48 Inverse of a 3x3 matrix, Gauss-Jordan elimination 01:30:09 Solving linear systems by matrix inversion 01:31:54 Inverse and powers of diagonal matrices 01:34:15 Triangular matrices 01:38:40 Symmetric matrices 01:40:24 Matrix determinant 01:49:09 Determinant by Gaussian elimination 01:53:25 Inverse using the adjoint matrix 01:57:23 Cramer's rule 02:02:13 Vectors in 2D and 3D space 02:14:48 Vectors in n-space 02:25:02 Norm of a vector in n-space, standard unit vectors 02:32:39 Dot product in n-space 02:53:11 Orthogonality and projection 03:04:00 Cross product and triple scalar product 03:25:09 Real vector spaces 03:44:21 Vector subspaces, span and linear combinations 04:09:13 Linear independence, examples 04:24:20 Basis for a vector space, coordinate vectors 04:45:13 Dimension of a vector space 04:54:47 Change of basis, mapping and the transition matrix 05:21:32 Row space, column space and null space 05:52:22 Rank and nullity of a matrix 06:11:08 Matrix transformations, operators 06:42:11 Compositions of matrix transformations 👉 Make sure to check out our full playlist on Linear Algebra Course. ⏩Playlist Link: • Introduction, Linear Equations - Linear Al... – Don’t forget to Like, Share & Subscribe for more deep-dive Linear Algebra Learnings. 🔴Subscribe: / @drofeng What part of Linear Algebra surprised you most? Comment below!👇 _______________________ 💥 Follow us on Social Media 💥 🎵TikTok: https://www.tiktok.com/@drofeng?lang=en 𝕏: https://x.com/DrOfEng 🥊: https://rumble.com/user/DrOfEng _______________________ Linear Algebra Full Course: Beginner to Advanced Linear Algebra (14hours Linear Algebra Mastery) #linearalgebra #calculus #algebra #maths #mathematics #math #science #education #mathskills #learning #stem #MathTutorial #STEMEducation #Matrices #MathHelp #CollegeMath #VectorSpaces #MathCourse #StudyWithMe #FullCourse #STEMEducation #StudyWithMe #FullCourse _______________________ 📌Keywords: linear algebra full course beginner to advanced linear algebra tutorial how to solve systems of linear equations matrix inversion explained vector spaces and subspaces overview what is row echelon form understanding basis and dimension in linear algebra null space vs column space explained linear independence and rank explained matrix transformations projection rotation reflection Gaussian elimination vs Gauss-Jordan method ______________________