Solution of Non-homogenous Systems

Consider the system: .

Methods

Method 1: Direct approach

Used when coefficient matrix is invertible. It means the system has a unique set of solutions.

Method 2: Cramer’s Rule

Let , where is the coefficient matrix and .

Where is the matrix obtained by replacing th column in matrix by .

Method 3: Reducing to Echelon Form

Start with . Convert the to echelon form. The solution can be found easily. If a contradiction is encountered while solving the equation, then the system has no solutions.