An Elementary Treatise On Determinants With Their Application to Simultaneous L
An Elementary Treatise On Determinants With Their Application to Simultaneous L
Carroll, Lewis, 1832-1898
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XVIIL] Equations. Iyi iy^i - 2, i \n-\-k, (i\ n — \ . A + i\ n-\-r-\-\ ) 57 nVi n\n — 2, n\ii + k, \n'\ ^n — 'i . A + n \n-\-r-\- 1 j n\\ n\v, — 2, n\ n + Jc, n\ii — 1 . A + + iyi i \n - 2, -] \n + k, i \n-{-r+\ u t\l n \ti — 2, n \n + k, n\ ^n + r + l do. ; . • . The Equations are inconsistent ; which is contrary to the hypothesis ; (Prop. III. . -. The square Blocks, formed by taking the first n — 2 columns, along with one of the columns from the w*!^ to the n + if^\ and with the last column,... are all evanescent ; and the same thing may be proved for any n — 2 of the first 7i—l columns ; . '. The square Blocks, formed by taking any 7i — 2 of the first n — 1 columns, along with any one of the next ;•+! columns, and with the last column, are all evanescent. Fourthly, let l\l l\7i-2, ^ \n+k, l\^+/ n\l n\n — 2, ii\n + k, n'\n + I ?^0; wherein k and I are any 2 of the numbers 0, \, . .. R ; let Xnj^i have the arbitrary value, 1, assigned to it ; and let each of the other Variables A\^, .
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