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kth
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Examples of in a sentence
We may say that, in the resulting determinant, the element in the ith row and k th column is obtained by multiplying the elements in the kth row of the first determinant severally by the elements in the ith row of the second, and has the expression aklb11+ak2b12+ak3b13��� +aknbin, and
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X n/ yl, Y2,...y n j ' x 1, � Forming the product of the first two by the product theorem, we obtain for the element in the ith row and kth column aZ, ayl az i ayz azi ayn ayl + e +...+ where or as a21 a22 ���a2,i -1 a2,i +1 .��a2n a31 ���a3,i -1 a3,ti+ 1
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(f, 4)) k +(f, 4)) k +�(f, 4/) k +a�(1, 4)')k; and, moreover, if we require to find the kth transvectant of one linear system of forms over another we have merely to multiply the two systems, and take the k th transvectant of the separate products.
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It is essentially an operation performed upon the product of �two forms. If, then, we require the transvectants of the two forms f+Xf', 0+14', we take their product fc5+xf'95+,-ifct'+atif'cb', and the kth transvectant is simply obtained by operating upon each term separately, viz.
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