Consider a non-homogeneous system of linear equations representing mathematically an overdetermined system. Such a system will be A. consistent having a unique solution B. consistent having many solutions C. inconsistent having a unique solution D. inconsistent having no solution

The correct answer is: D. inconsistent having no solution

A non-homogeneous system of linear equations is a system of equations in which the number of equations is greater than the number of unknowns. If the system is overdetermined, then there are more equations than there are unknowns, and the system will have no solution.

A consistent system of linear equations is a system of equations in which there exists at least one set of values for the unknowns that satisfies all of the equations. An inconsistent system of linear equations is a system of equations in which there does not exist any set of values for the unknowns that satisfies all of the equations.

A system of linear equations with a unique solution is a system of equations in which there is only one set of values for the unknowns that satisfies all of the equations. A system of linear equations with many solutions is a system of equations in which there are more than one set of values for the unknowns that satisfies all of the equations.

In the case of an overdetermined system of linear equations, there are more equations than there are unknowns. This means that there is no set of values for the unknowns that will satisfy all of the equations. Therefore, the system is inconsistent and has no solution.