What is an augmented matrix?

An augmented matrix is defined as a matrix that results from combining a coefficient matrix with a constant vector, typically in the context of solving systems of linear equations. This representation is particularly useful when applying methods such as Gaussian elimination or Gauss-Jordan elimination to find solutions for these systems.

When working with a system of linear equations, the coefficient matrix consists of the numbers that multiply the variables in the equations, while the constant vector contains the values from the right-hand side of the equations. By appending the constant vector to the coefficient matrix, we form the augmented matrix, which allows for a unified approach to manipulating the entire system as a single entity.

This construction is essential in applied linear algebra as it simplifies the process of solving systems and visualizes the relationship between the variables and their corresponding constants. The other provided choices do not accurately capture the meaning of an augmented matrix in this context.