In Exercises 9-12, write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables.

An augmented matrix is a matrix that represents a system of linear equations, where each row corresponds to an equation and the last column represents the constants from the right-hand side of the equations. It combines the coefficients of the variables and the constants into a single matrix, facilitating the use of row operations to solve the system.

A system of linear equations consists of two or more linear equations that share the same variables. The solution to the system is the set of values for the variables that satisfy all equations simultaneously. Systems can have one solution, no solution, or infinitely many solutions, depending on the relationships between the equations.

Row operations are techniques used to manipulate the rows of a matrix to simplify it, particularly in the context of solving systems of equations. The three primary row operations are swapping two rows, multiplying a row by a non-zero scalar, and adding or subtracting the multiple of one row to another. These operations help in transforming the augmented matrix into a form that makes it easier to extract the solutions.