Final answer:
Statement (b) about Cramer's rule being limited to 2x2 and 3x3 systems is not true. Cramer's rule uses determinants and is applicable to systems of any size, provided the system has an equal number of linear equations and unknowns, and the determinant of the coefficient matrix is non-zero.
Step-by-step explanation:
The question pertains to Cramer's rule which is a theorem in linear algebra used to solve systems of linear equations. When considering the statements provided in the question:
- (a) It involves determinants - Cramer's rule indeed uses determinants to find the solution of the system.
- (b) It is limited to 2x2 and 3x3 systems - This is not true. While Cramer's rule is often taught using 2x2 and 3x3 systems, it can be applied to systems of any size as long as the system has the same number of equations as unknowns and the determinant of the coefficient matrix is non-zero.
- (c) It provides a unique solution - This is true, but only if the determinant of the coefficient matrix is non-zero.
- (d) It requires matrix inversion - This is not true. Cramer's rule does not require matrix inversion; it instead requires the calculation of determinants for the matrix and its column-modified counterparts.
Therefore, statement (b) about Cramer's rule being limited to 2x2 and 3x3 systems is not true, as it is applicable to systems of any size with the aforementioned conditions.