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When operations are to be performed on the same elementary row in a specific matrix, the columns of the two matrices are appended forming an augmented matrix. Three-row operations are usually performed on the augmented matrix to yield the system equations. The three elementary operations are switching any two rows, multiplying a row by a constant and adding one row to another.When switching any two rows we obtain the followingWhen multiplying a row with a constant we obtain the followingWhile when multiplying a row with a constant we obtain the followingThe main advantage of converting the system matrix to an augmented matrix is that it helps in obtaining solutions for systems of linear equations. Also, the solutions can be run even if the system matrix is converted to augmented matrix since it changes it to a minimum row-echelon. This is because it converts the system matrix into a reduced. Systems in the physical state are usually represented in matrix form in a digital scale. Therefore, when a matrix of a system is multiplied by a scalar, the result obtained will be called a scalar multiplication, while on the other hand, when a matrix of a system is multiplied by another matrix of another system, say the system needs to merge to produce the same output, then the result is known as matrix multiplication.Some operations, in as far as augmented matrix operations are concerned, do not make sense, for example when the values of two numbers in the last row are zero, meaning that the system does not have a solution, meaning it cannot work. Another example is when you have all zeros in the last row. This means that the system can have infinitely many solutions. These cases do not make sense physically. Works CitedWu, Meng-Lun, Chia-Hui Chang, and Rui-Zhe Liu. "Integrated perception of the implementation Of the augmented matrices."Expert Systems with Applications42.6 (2014) 2454-2501....

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