Final answer:
To find the solution set of a system of linear equations represented by an augmented matrix, perform row operations to transform the matrix into row-echelon form or reduced row-echelon form. The solution set depends on the outcome of these operations.
Step-by-step explanation:
To find the solution set of a system of linear equations represented by an augmented matrix, we need to perform row operations to transform the matrix into row-echelon form or reduced row-echelon form. The solution set will depend on the outcome of these row operations.
If the row-echelon form has a row of the form [0 0 0 ..., b], where b is nonzero, then the system has no solution. If the row-echelon form has more variables (unknowns) than nonzero rows, then the system has infinite solutions. Otherwise, the system has a unique solution.
To illustrate this process, let's consider an example:
Augmented matrix:
[1 2 3 | 4]
[5 6 7 | 8]
[9 10 11 | 12]
We perform row operations to transform the matrix into row-echelon form:
[1 2 3 | 4]
[0 -4 -8 | -12]
[0 0 0 | 0]
In this case, we have a row of the form [0 0 0 | 0] and two variables with nonzero rows, so the system has infinite solutions.