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?
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?
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Singular matrices lead to either no solutions or infinitely many solutions, depending on the consistency of the system.
Updated On: Mar 17, 2025
- The system is inconsistent
- The system has a unique solution
- The system is consistent and has no solution
- The system has infinitely many solutions
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The Correct Option is D
Solution and Explanation
If A is a singular matrix and B is a null matrix, it implies that the system of equations has infinitely many solutions. This is because a singular matrix means that the system does not have a unique solution, but since B is a null matrix, there are multiple solutions that satisfy the equation.
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