...term. 400. General Definition. In general, a determinant of the nth order is an expression involving n' elements arranged in n rows of n elements each ; the...sections), and take the sum of all these / products. Nearly all the properties of determinants can be obtained directly from this definition and the rule...

...general, a determinant of the iith order is an expression involving ri> elements arranged in n rows of и elements each ; the expansion, that is, the expression...sections), and take the sum of all these products. Nearly all the properties of determinants can be obtained directly from this definition and the rule...

...general, a determinant of the nth order is an expression involving тг2 elements arranged in n rows of и elements each ; the expansion, that is, the expression...prefix to each of the products thus formed either -for — (which sign is to be determined by a rule to be given in the following sections), and take...

...suffixes 1, 2, 3, ---n, but none of the letters or suffixes twice repeated ; hence, every term contains one and only one element from each row, and one and only one element from each column of the matrix. 384. If in a matrix of a determinant the letters a, b, c,---l and the numbers 1, 2,...

...ALGEBRA. and aja - aAc, + аА«, - <Ч5А + а,» А - aA<i ai <Ч Al »Vir ¿ь£\ Ы^ К is written Form all the possible products of n elements each...sections), and take the sum of all these products. Nearly all the properties of determinants can be obtained directly from this definition and the rule...

...a time, ", <4. «n,2) «»,3) "•> "n," subject to the restriction that each product shall contain one and only one element from each row, and one and only one from each column, writing the first suffixes in the order 2, 3, ••-, n, and making each product...

...с, ( a4 64 c4 i is a determinant of the fourth order, and it is equal to the sum of all the products that can be formed by taking one, and only one, element from each column and from each row, considering the sign of each product positive if it contains an even number...

...the symbol Ci dl is a determinant of the fourth order, and it is equal to the sum of all the products that can be formed by taking one, and only one, element from each column and from each row, considering the sign of each product positive if it contains an even number...

...<»i «2 (6) of determinants of orders 2 and 3 respectively, consists (except for sign) of the product formed by taking one and only one element from each row and column. This fact suggests the extension of determinants to represent certain expressions in n* elements...

...possible products of the elements of the determinant, such that each product shall have as factors one and only one element from each row, and one and only one from each column. 2. Arrange the elements in each product so that the first subscripts are h1 the order...