Final answer:
A system with a 4 x 8 coefficient matrix and four pivot columns is consistent because there are pivot positions in each row, indicating no contradictions and at least one solution exists.
Step-by-step explanation:
The question asks if a system with a 4 x 8 coefficient matrix that has four pivot columns is consistent. In linear algebra, if a coefficient matrix associated with a system of linear equations has a pivot position in each row, it implies that there are no rows that represent a contradiction (such as 0 = 1) which would make the system inconsistent.
Since the matrix has four pivot columns and presumably four rows (as the number of pivot positions cannot exceed the number of rows), it means that each row has a pivot position, indicating that every linear equation in the system has a leading variable and hence, the system does not have any contradictions. Therefore, this would imply that the system is consistent, meaning that there is at least one set of solutions to the system of equations.