Appropriate use of elementary row or column operations can strongly simplify the calculation of determinants, so we shall examine them with some detail.
Consider the matrix . Adding -1 times row 4 to row 2 and, successively -2 times row 4 to row 3 we obtain: . Using cofactor expansion by column 3, we have: det(A) = . Now adding -1 times column 3 to column 1 and .1 times row 1 to row 3, we have: . So we obtain . Finally, adding 1 times row 1 to row 2 we find: . We can easily conclude that det(A)=-34.