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Unique Solution Example: System of Non homogeneous linear equations

The video explains how to solve a system of non-homogeneous linear equations using the rank method (0:00). Here's a breakdown of the steps: • Forming the Augmented Matrix The first step is to create an augmented matrix (0:28) by combining the coefficient matrix and the column vector of constants (0:19). • Finding the Rank Next, the video demonstrates how to find the rank of the augmented matrix using the equivalent method (0:39). This involves transforming the matrix to an equivalent form where elements below the main diagonal are zero (0:41). Operations like multiplying rows by -1 (1:26) and interchanging rows (1:51) are used to simplify the matrix. • Determining Consistency and Solution Type Once the matrix is in an equivalent form, the rank of the augmented matrix and the rank of the coefficient matrix are compared (2:33). If both ranks are equal and also equal to the number of variables, the system is consistent (3:19) and has a unique solution (3:46). • Back Substitution Finally, the video shows how to use back substitution (4:21) to find the values of x, y, and z, which represent the unique solution to the system (4:23). The speaker also demonstrates how to cross-check the solution by plugging the values back into the original equations (4:51). Solving System of non homogeneous Linear Equations using Rank Method System of linear equations Solving system of linear equations (non-homogeneous and homogeneous) Solving system of linear equations using matrices Solving system of linear equations using inverse of augmented matrix intermediate Consistent and inconsistent system Consistent and inconsistent system of non homogeneous linear equations Unique solution of system of non-homogeneous linear equation using rank method Unique solution of system of linear equations infinite solution of system of linear equations no solution of system of linear equations Rank of a matrix using echelon form    • How to find Rank of a Matrix | Echelon For...