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440 Rh Of these four determinants the first three vanish, Art. 548; thus the expression reduces to the last of the four determinants; hence its value

Ex. 2. Find the value of |67 19 21]. 39 13 14 81 24 26.

We have

67 19 21/=|10+457 19 21{=/10 19 21)+4/57 19 21 39 13 14 O+ 30 13 14 0 13 14 39 13 ie [81 24 26) 9472 24 26 9 24 26 ke 24 26 ={10 19 21|=/10 19 19-4-2)> 1009s =10/13 1/49 - : = 20 — 63 =— 43. 24 2)
 * 0 13 14 0 13 1341 0B 1
 * 9 24 26 9 24 2442 9 24 2

551. Simplification of Determinants. Consider the determinant

as in the last article we can show that it is equal to

and the last two of these determinants vanish [Art. 549, Cor.]. Thus we see that the given determinant is equal to a new one whose first column is obtained by subtracting from the constituents of the first column of the original determinant equimultiples of the corresponding constituents of the other columns, while the second and third columns remain unaltered. Conversely,