In a system of linear equations, coefficient determinant of the unknown is zero.Select one:TrueFalse

To determine the truth of the statement, we need to analyze the implications of a coefficient determinant being zero in a system of linear equations.

True or False Analysis

1. Understanding Determinants: In linear algebra, the determinant of a coefficient matrix provides insight into the properties of a system of linear equations. If the determinant is non-zero, the system has a unique solution.

2. Coefficient Determinant Equals Zero: If the coefficient determinant of the unknowns is zero, it indicates that the system is either inconsistent (no solutions) or dependent (infinitely many solutions).

3. Conclusion: The statement can be interpreted to mean that if the determinant is zero, we cannot expect a unique solution. Thus, the statement is true in the context of linear systems.

Final Answer

True. If the coefficient determinant of the unknown is zero, it indicates that the system does not have a unique solution.