Question

In the system of linear equations AX = B, if A is a singular matrix and B is a null matrix, then which of the following is correct?

• A. The system is inconsistent
• B. The system has a unique solution
• C. The system is consistent and has no solution
• D. The system has infinitely many solutions

Hint:

Singular matrices lead to either no solutions or infinitely many solutions, depending on the consistency of the system.

Answer 1

The Correct Option is D

A system of equations with a singular matrix A and a null matrix B necessarily yields infinitely many solutions. This is because a singular matrix A precludes a unique solution, and the null matrix B ensures that multiple solutions exist.