Consider a system of three linear equations in three variables represented in matrix form as AX=B, where A is a 3×3 matrix and B is a 3×1 column matrix.
(i) State the conditions on ∣A∣ and (adjA)B for the system to have
(a) a unique solution,
(b) no solution, and
(c) infinitely many solutions.
(ii) Give a brief justification for each of the three conditions stated in part (i).