NON-HOMOGENEOUS LINEAR ALGEBRAIC EQUATIONS
Non-Homogeneous Systems of Linear Algebraic Equations A non-homogeneous system of linear equations with an coefficient matrix consists of linear equations and unknown variables, represented as: Matrix Representation This system can be compactly expressed in matrix form: where: (Coefficient Matrix, ): (Vector of Unknowns, ): (Constant Vector, ): Standard Form where is an matrix, is the vector of unknowns, and is a non-zero constant vector. Existence and Types of Solutions Let be the augmented matrix, be the rank of the coefficient matrix, and be the number of variables: Inconsistent (No Solution): Consistent with a Unique Solution: Consistent with Infinitely Many Solutions: Problems: 1. solve the system of linear equations: sol: Given linear system of non-homogeneous equation St...