Consistency of System of Linear Equations: Solved Problem 20 📝 | Most Difficult Sum

⚡ Consistency of System of Linear Equations: Solved Problem 20 📝 | Most Difficult Sum In this video (Lecture 20), we learn how to test for the consistency and inconsistency of a matrix for a system of linear equations. We are solving a 4x4 non-homogeneous linear system, which is one of the most important and difficult sums in Engineering Mathematics and Class 12 Algebra. This step-by-step tutorial covers how to find the rank of an augmented matrix [A|B] using Echelon form and determine if the system has a unique solution, infinite solutions, or no solution (inconsistent). ⏱️ TIMESTAMPS: 00:00 - Introduction & Theorem Rules 04:24 - Writing the Augmented Matrix [A|B] 06:48 - Applying Row Transformations (Echelon Form) 20:24 - Finding Rank & Testing for Consistency 26:37 - Final Solution Vector (x1, x2, x3, x4) 💡 Topics Covered in this Video: • How to check consistency of linear system of equations • Consistent and inconsistent system of linear equations examples • Linear algebra exercises and solved problems in matrix • How to find the rank of a 4x4 matrix using echelon form 📺 WATCH ALL PREVIOUS LECTURES: Please visit the Playlist section on my channel to watch all matrices tutorials. 📖 STUDY TIP: Please keep practicing and solve all these linear algebra exercises in a dedicated practice notebook to build speed and accuracy. 📣 If you found this video helpful, please SUBSCRIBE to Tikle's Academy of Maths, hit the BELL icon for updates, LIKE the video, and SHARE it with your engineering friends. If you have any doubts, leave a comment below! #consistencyofmatrix #engineeringmaths #matricesquestion #systemoflinearequations #rankofmatrix #matrixsolvedproblems #tiklesacademyofmaths #linearalgebra