“Cramer's rule”的概念、定义、习题解题方法及翻译-数学辞典

单词

Cramer's rule

释义

Cramer's rule

Consider a set of n linear equations in n unknowns x1, x2,…, xn, written in matrix form as Ax = b. When A is invertible, the set of equations has a unique solution x = A−1b. Since A−1 = (1/detA) adjA, where adjA is the adjoint of A, this gives the solution

which may be written

using the entries of b and the cofactors of A. This is Cramer's rule. Computationally Cramer's rule is highly inefficient compared with Gaussian elimination.

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