The Math Problems from Good Will Hunting, with Solutions

From Wikipedia: "Consider a system of n linear equations for n unknowns, represented in matrix multiplication form as Ax = b where the n × n matrix A has a nonzero determinant, and the vector x = {x_1, x_2, ..., x_n}^T is the column vector of the variables. Then Cramer's rule states that in this case the system has a unique solution, whose individual values for the unknowns are given by: x_i = det(A_i)/det(A)"