Suppose a nonhomogeneous system of fivefive linear equations in sixsix unknowns has a solution, with oneone free variablevariable. Is it possible to change some constants on the equations' right sides to make the new system inconsistent? Explain. Choose the correct answer below. A. No. Consider the system as Axequals=b, where A is a 55times×66 matrix. Then, dim Nul Aequals=11 and dim Col Aequals=rank Aequals=66minus−dim Nul Aequals=55. Since Col A is a subspace of set of real numbers RℝSuperscript 55, Col Aequals=set of real numbers RℝSuperscript 55. So every vector b in set of real numbers RℝSuperscript 55 is also in Col A, and Axequals=b has a solution for all b. B. Yes. Consider the system as Axequals=b, where A is a 55times×66 matrix. Then, dim Nul Aequals=11 and dim Col Aequals=rank Aequals=66minus−dim Nul Aequals=55. Since Col A is a subspace of set of real numbers RℝSuperscript 66, Col Aequals=set of real numbers RℝSuperscript 66. Since dim Col Aequals=set of real numbers RℝSuperscript 55 is a proper subspace of set of real numbers RℝSuperscript 66, it is possible to find vectors b for which the equation is not satisfied. C. No. For any matrix equation Axequals=b, if there exists at least one vector b that satisfies the equation and the solution contains at least one free variable, then every vector b must be a solution to the system. D. Yes. For any matrix equation Axequals=b, it is possible to find vectors b for which the equation is not satisfied.