Скачать или смотреть Math Visual Proof Cramer's Rule

Cramer's Rule is a method in linear algebra used to solve a system of linear equations with the same number of equations as unknowns, provided the system has a unique solution. It works by expressing each variable as a ratio of determinants. For a system AX = b, where A is a square coefficient matrix and b is the constant vector, the solution for the i-th variable is given by det(A_i) / det(A). Here, det(A) is the determinant of the coefficient matrix, and det(A_i) is the determinant of the matrix obtained by replacing the i-th column of A with the constant vector b. Cramer's Rule is elegant and straightforward, but it is practical only for small systems, since computing determinants of large matrices can be computationally expensive.

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