Linear Algebra

For a system of linear equations represented as , the determinant and the adjugate of play a key role in determining the consistency of the system. 1. If , the matrix is invertible, and the system is consistent. The solution is given by: 2. If , the system may be inconsistent or have infinitely many solutions, depending on whether . If , the system has no solution (inconsistent); otherwise, there may be infinitely many solutions. 3. If , the system is always consistent with a unique solution. Thus, the correct answer is (D) May or may not be consistent if and .