אלגברה לינארית | משוואות ממעלה ראשונה (ומטריצות) | תרגיל 2

Welcome back to the Linear Algebra course for undergraduate students! After we made a soft landing in the previous video and understood the basics, this time we're stepping up and getting to the heart of the matter. In this video, we'll solve Exercise #2 together: A more complex system of **three equations with three unknowns This is exactly the stage where high school methods become impossible, and this is where the real academic tool – the matrix – comes into play and saves us. We'll learn how to take the system, translate it neatly into an expanded matrix, and perform a series of clever algebraic row operations to zero the terms below the main diagonal. We'll understand how to get to the desired graduated form, and from there extract the values ​​of the unknowns one after the other (using the backward substitution method). The bonus of this video: At the end of the solution, I'll show you how to do a quick self-test on the test to be 100% sure that your answers are correct, so you can leave the test with a clear head and a high score! Grab a piece of paper, a pen, and a calculator, and let's break down this matrix together step by step. If the video helped you sort out the mess, be a friend - click the like button, subscribe to the channel so you don't miss the next exercises, and share in the degree group so that others will finally understand the material. Good luck! 0:00 Introduction and presentation of Exercise 2 (3 equations with 3 unknowns) 0:42 Building the expanded matrix from the system of equations 1:50 Planning the ranking strategy: How to choose which term to zero first 3:05 Performing first row operations and zeroing the first column 5:50 Moving to the second column and bringing the matrix to a ranked form 8:10 Extracting the first unknown (z) from the row of zeros 9:04 Substituting backwards to find the additional unknowns (y and x) 11:05 My tip for the test: How to perform a quick self-check and make sure we were right 12:12 Summary and look ahead to the next exercise #linear_algebra #matrices #gaussian_method #system_of_equations #three_unknowns #matrix_ranking #students #bachelor's_degree #academic_mathematics #exercise_solution #online_learning