Final answer:
The linear system corresponding to an augmented matrix has a solution if the system of equations it represents is consistent, meaning the equations intersect at one or more points. It has no solution if the equations do not intersect.
Step-by-step explanation:
Asking whether the linear system corresponding to an augmented matrix has a solution amounts to asking whether the system of equations represented by the matrix is consistent or inconsistent.
A linear system is consistent if it has at least one solution, meaning the equations intersect at one or more points. It is inconsistent if it has no solution, meaning the equations do not intersect.
For example, if the augmented matrix is:
[1 2 3 | 4
2 4 6 | 8]
The corresponding system of equations is:
1x + 2y + 3z = 4
2x + 4y + 6z = 8
By solving this system, we can determine whether it has a solution or not.