Gaussian elimination can be used to efficiently evaluate a determinant, as follows. Divide each element of row 1 of the determinant (8.20) by (11 and place the factor (11 in front of the determinant (Theorem IV of Section 8.3). Then subtract the appropriate multiples of the row 1 elements from row 2, row 3, ( ( ( ( row n to make (21, (31, ( ( ( ( (n1 zero (Theorem V). Next divide the second-row elements by the current value of (22 and insert the factor (22 in front of the determinant, and so on. Ultimately, we get a determinant all of whose elements below the principal diagonal are zero. From Prob. 8.20, this determinant equals the product of its diagonal elements. Use this procedure to evaluate the determinant in Prob. 8.19b.