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Cramer's rule is useful for reasoning about the solution, but, except for n = 2 or 3, it is rarely used for computing a solution, since Gaussian elimination is a faster algorithm. The determinant of an endomorphism is the determinant of the matrix representing the endomorphism in terms of some ordered basis.
However, in 1702 Leibniz erroneously said that no polynomial of the type x 4 + a 4 (with a real and distinct from 0) can be written in such a way. Later, Nikolaus Bernoulli made the same assertion concerning the polynomial x 4 − 4 x 3 + 2 x 2 + 4 x + 4 , but he got a letter from Euler in 1742 [ 4 ] in which it was shown that this polynomial ...