Cramer’s formula

Simultaneous linear inhomogeneous equations can be solved with various techniques, including elimination, use of Cramer s formula, and by matrix inversion. 

Numerical methods, which are suitable for solving practical calculation problems, but which if not included here will have to be looked up in textbooks or notes every time they are used (Newton-Rapson iteration, Cramer s formula, etc.). 

Linear equation systems of the form Ax = b are conventional in practical calculation problems. For solution of such equation systems by pocket calculator, one can benefit from Cramer s formula in case of two or three unknowns. The advantage in this solution method is, for example, that keying and calculation can be performed in a simple and systematic manner. 

Cramer s formula can be generalized for all n > 2. However, as a solution method, the formula is less suitable for n > 3. For three equations with three imknowns (xi,X2,X3), the solution is determined by... 

As mentioned, Cramer s formula is only suitable for solving equation systems with two or three unknowns the advantage using this solution method is the clear systematics when keying on a pocket calculator. To solve linear equation systems with more unknowns than three, we can, for example, use Gauss elimination. 

In the quantum formalism, with a finite number of reactant states, Eq. (28) can be solved by Cramer s rule, thereby leading to a determinantal formula for 1. Such a formula was given by Kim, though Z did not appear in it because the completeness condition of Eq. (9) was not used. 

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