Answer: Cramer's rule is a method for solving systems of linear equations by using determinants. To use Cramer's rule, you first need to set up the system of equations in matrix form, like so:
[A][x] = [b]
where [A] is the coefficient matrix of the system, [x] is the vector of unknowns, and [b] is the vector of constants.
To apply Cramer's rule, you can solve for each unknown in [x] by calculating the determinants of a series of matrices that are formed by replacing one column of [A] at a time with the constants in [b]. Specifically, the solution for the ith unknown is given by:
xi = det([A]i) / det([A])
where [A]i is the matrix formed by replacing the ith column of [A] with the constants in [b], and det([A]) is the determinant of the original matrix [A].
To calculate the determinants, you can use any method you prefer, such as row reduction or cofactor expansion. Note that Cramer's rule only works for systems of linear equations with the same number of equations as unknowns, and it can be computationally expensive for large systems.
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