Question

When using Cramer's Rule to solve a system of equations, if the determinant of the coefficient matrix equals zero and at least one numerator determinant is zero, then the system _____________________.

A. is consistent
B. is dependent
C. is inconsistent
D. has no solution

Answer 1

B. is dependent

Explanation:

The denominator determinant will be zero when the coefficients of the variables are dependent. One of the numerator coefficients will be zero when the coefficients involved are dependent. Hence using Cramer's Rule will result in the ratio 0/0 when the system is dependent.

___

The ratio will be 1/0 if the system is inconsistent (has no solution).