Example:
(i) Note that the entries in a given matrix need not be distinct. (ii) The entries in this matrix are function of x. A matrix having m rows and n columns is called as matrix of order mxn. Such a matrix has mn elements. In general, an mxn matrix is in the form Where a i j represents the ele..
(i) Note that the entries in a given matrix need not be distinct. (ii) The entries in this matrix are function of x. A matrix having m rows and n columns is called as matrix of order mxn. Such a matrix has mn elements. In general, an mxn matrix is in the form Where a i j represents the ele..Matrices and Determinants Animation
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Permutations and Combinations..Suggested answer:
4. Sum the following: i) 1.2 + 2.4 + 3.8 +.... to n ter..
4. Sum the following: i) 1.2 + 2.4 + 3.8 +.... to n ter..Examples:
Each one of the following series form an A.P. i) 1, 3, 5, 7, ii) 3, 7, 11, 15, iii) 15, 12, 9, iv) x, x - d, x - 2d, ..... The common difference is found by subtracting any term of the series from the immediate succeeding term. In the above example, common difference in the first is 2, in the..
Each one of the following series form an A.P. i) 1, 3, 5, 7, ii) 3, 7, 11, 15, iii) 15, 12, 9, iv) x, x - d, x - 2d, ..... The common difference is found by subtracting any term of the series from the immediate succeeding term. In the above example, common difference in the first is 2, in the..Proof:
. Proceeding in this way, we see that there are n(n-1)(n-2)(n-3)(n-4)....[r factors] different ways of filling r blank spaces with n letters. The r t h factor = n - (r -1) = n - r = 1. The number of r-permutations of n different things is n P r = P(n,r) = n(n-1) (n-2) (n-3)...(n - r +..
. Proceeding in this way, we see that there are n(n-1)(n-2)(n-3)(n-4)....[r factors] different ways of filling r blank spaces with n letters. The r t h factor = n - (r -1) = n - r = 1. The number of r-permutations of n different things is n P r = P(n,r) = n(n-1) (n-2) (n-3)...(n - r +..Question 2
= (32.16.8.4.2)(33.31.30.18.17.15.14.13.12.11.10....3.1) = (2 5 .2 4 .2 3 .2 2 .2 1 )(33.31.30.....3.1) which is divisible by 2 1 5 . vi) (n! + 1) is not divisible by any natural number between 2 and ..
= (32.16.8.4.2)(33.31.30.18.17.15.14.13.12.11.10....3.1) = (2 5 .2 4 .2 3 .2 2 .2 1 )(33.31.30.....3.1) which is divisible by 2 1 5 . vi) (n! + 1) is not divisible by any natural number between 2 and ..See what our Users say :
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