Higher Algebra: A Sequel to Elementary Algebra for Schools |
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Page xx
... columns Development of determinant of third order Sign of a determinant is altered by interchanging two adjacent rows or columns . If two rows or columns are identical , the determinant vanishes A factor common to any row or column may ...
... columns Development of determinant of third order Sign of a determinant is altered by interchanging two adjacent rows or columns . If two rows or columns are identical , the determinant vanishes A factor common to any row or column may ...
Page 52
... columns , one consisting of the first n natural numbers , and the other of their squares . .. the sum = Σn2 + Σn = = n ( n + 1 ) ( 2n + 1 ) 6 n ( n + 1 ) ( 2n + 1 2 3 n ( n + 1 ) ( n + 2 ) n ( n + 1 ) + 2 + 1 } Example 2. Sum to n terms ...
... columns , one consisting of the first n natural numbers , and the other of their squares . .. the sum = Σn2 + Σn = = n ( n + 1 ) ( 2n + 1 ) 6 n ( n + 1 ) ( 2n + 1 2 3 n ( n + 1 ) ( n + 2 ) n ( n + 1 ) + 2 + 1 } Example 2. Sum to n terms ...
Page 117
... columns and cancel like factors from each side , and we obtain " P , = - - = n ( n − 1 ) ( n − 2 ) . - ...... ( n − r + 1 ) . Example 1. Four persons enter a railway carriage in which there are six seats ; in how many ways can they ...
... columns and cancel like factors from each side , and we obtain " P , = - - = n ( n − 1 ) ( n − 2 ) . - ...... ( n − r + 1 ) . Example 1. Four persons enter a railway carriage in which there are six seats ; in how many ways can they ...
Page 129
... columns and cancel like factors from each side ; thus 156 . " C. = n ( n - 1 ) ( n - 2 ) ...... ( n − r + 1 ) r ( -1 ) ( -2 ) ...... 1 To find the total number of ways in which it is possible to make a selection by taking some or all ...
... columns and cancel like factors from each side ; thus 156 . " C. = n ( n - 1 ) ( n - 2 ) ...... ( n − r + 1 ) r ( -1 ) ( -2 ) ...... 1 To find the total number of ways in which it is possible to make a selection by taking some or all ...
Page 409
... columns , and in its expanded form each term is the product of two quantities ; it is therefore said to be of the second order . The letters a1 , b1 , a , b , are called the constituents of the determinant , and the terms a , b ,, a , b ...
... columns , and in its expanded form each term is the product of two quantities ; it is therefore said to be of the second order . The letters a1 , b1 , a , b , are called the constituents of the determinant , and the terms a , b ,, a , b ...
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Other editions - View all
Higher Algebra: A Sequel to Elementary Algebra for Schools H. S. Hall,S. R. Knight No preview available - 2017 |
Higher Algebra: A Sequel to Elementary Algebra for Schools (Classic Reprint) H. S. Hall No preview available - 2017 |
Higher Algebra: A Sequel to Elementary Algebra for Schools H. S. Hall,S. R. Knight No preview available - 2018 |
Common terms and phrases
a+b+c+ a₁ Algebra annuity arithmetic mean arithmetical progression ascending powers ax² b₁ Binomial Theorem C₁ C₂ complete quotient compound interest continued fraction cube root denominator denote digits divisible Elementary Algebra equal equation x² Example expression factors Find the coefficient find the number Find the sum find the value finite geometrical progression given log given series greater greatest term hence infinite series less letters limit logarithms multiplying negative nth term number of solutions number of terms Ny² obtain orders of differences P₁ partial fractions positive integers preceding article proper fraction prove quadratic quadratic equation r+1)th term radix ratio rational integral function recurring series scale of relation series is convergent series is divergent shew solution in positive Solve suppose u₁ U₂ unity vergent whence zero
Popular passages
Page 61 - ... any number divided by 9 will leave the same remainder as the sum of its digits divided by 9.
Page 175 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 117 - The number of combinations of n things г at a time is equal to the number of combinations of n things n—r at a time.
Page 454 - If then we suppose the factors corresponding to the negative and imaginary roots to be already multiplied together, each factor x— a corresponding to a positive root introduces at least one change of sign ; therefore no equation can have more positive roots than it has changes of sign. To prove the second part of Descartes...
Page 11 - In any proportion the product of the extremes is equal to the product of the means. Let the proportion be a : b = с : d.
Page 367 - DEFINITION. If an event can happen in a ways and fail in b ways, and. each of these ways is equally likely, the probability, or the chance, of its happening is , and...
Page 492 - Geese, which were proceeding at the rate of 3 miles in 2 hours, he afterwards met a stage wagon, which was moving at the rate of 9 miles in 4 hours. B overtook the same drove of Geese at the 45th mile stone, and met the same stage wagon exactly forty minutes before he came to the 31st mile stone. Where was B when A reached London 1 Solution.
Page 178 - The integral part of a logarithm is called the characteristic, and the decimal part is called the mantissa.
Page 130 - There are n points in a plane, no three of which are in the same straight line with the exception of p, which are all in the same straight line; find the number of lines which result from joining them.
Page 486 - A railway train after travelling for one hour meets with an accident which delays it one hour, after which it proceeds at three-fifths of its former rate, and arrives at the terminus...