A matrix A is not invertible if and only if O is an eigenvalue of A. Choose the correct answer below O A. False. If 0 is an eigenvalue of A, then there are nontrivial solutions to the equation Ax 0x. The equation Ax=Ox is equivalent to the equation Ax 0, has nontrival solution if and only if A is invertible.
O B. False. If 0 is an eigenvalue of A, then the equation Ax=0x has only the trivial solution. The equation Ax=Ox is equivalent to the equation Ax=O and Ax=O has only the trival solution if and only if A is invertible.
○ C. True. If O is an eigenvalue of A, then the equation Ax=0x has only the trivial solution. The equation Ax=0x is equivalent to the equation Ax=0X and Ax=0 has only the trival solution if and only if A is not invertible.
○ D. True. If 0 is an eigenvalue of A, then there are nontrivial solutions to the equatioon Ax=0x. The equation Ax=0x is equivalent to the equation Ax==0, and Ax=0 has nontrival soluions if and only if A is not invertible.