Let A=(1224) be the coefficient matrix of a system of two linear equations in two variables. Which one of the following statements is TRUE about the system?
a) The system necessarily has a unique solution because detA=8=0.
b) Since the coefficient matrix is singular, the system must always have infinitely many solutions irrespective of the constants.
c) The system cannot have a unique solution; it may have infinitely many or no solution depending on the constant terms.
d) Because the rows of A are proportional, the system can never be consistent; hence it has no solution.