Final answer:
Option B is not true; Cramer's Rule uses determinants rather than augmented matrices and row echelon forms to solve systems of equations. It operates on the principle of calculating ratios of determinants for each variable in a system with an equal number of equations and unknowns.
Step-by-step explanation:
Among the given statements about Cramer's Rule, the one that is NOT true is this method uses augmented matrices and row echelon form to solve for the unknown variables. Cramer's Rule actually does not involve augmented matrices or row echelon forms but instead relies on calculating ratios of determinants to find the solutions to the system of linear equations.
To clarify, Cramer's Rule is applicable to a system of linear equations with the same number of equations as unknowns, and it requires the determinant of the coefficient matrix (det A) to be non-zero. If det A is zero and the determinant formed by the constants of the system (let's call it 'det B') is nonzero, then the system has no solution (option A). However, if det A, det B, and other determinants calculated for the system are all zero, the system may have infinitely many solutions, indicating it's dependent (option D). The actual method of Cramer's Rule uses the determinant of the coefficient matrix and other determinants obtained by replacing one column of the coefficient matrix with the constants from the equations to solve for each unknown variable.