... demands far more computation than the unavoidable minimum.Some matrix methods are far more efficient. Analytical applications ofCramer’s formula appear in Section 5.1.2 on the generalized geometric ... expansion of A by elements from row i and their cofactors isA =nj=1aijAij, 1 ≤ i ≤ n. (2.3.8)The expansion of A by elements from column j and their cofactors isobtained by summing over i instead ... when per-formed in reverse order on A3, have the same effect as premultiplication ofA3 by the unit determinant V3.12 2. A Summary of Basic Determinant TheorySimilarly, the column operationsCi=ij=1vijCj,vii=1,...