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From (1) and (2), (A + B) + C = A + (B + C) \ The associative law is verifi..
From (1) and (2), (A + B) + C = A + (B + C) \ The associative law is verifi..Examples:
skew-symmetric for every square matrix A. That is any square matrix is expressible as the sum of a symmetric matrix and a skew-symmetric matrix. 5. A matrix which is both symmetric and skew symmetric is a zero matr..
skew-symmetric for every square matrix A. That is any square matrix is expressible as the sum of a symmetric matrix and a skew-symmetric matrix. 5. A matrix which is both symmetric and skew symmetric is a zero matr..Example:
The matrices are identify matrices of order 2 and 3 respectivel..
The matrices are identify matrices of order 2 and 3 respectivel..Theorem:
The number of combinations of n dissimilar things, taken r at a time is..
The number of combinations of n dissimilar things, taken r at a time is..Note:
1. O!= 1 2. When n is a negative or fraction, n! is not defined...
1. O!= 1 2. When n is a negative or fraction, n! is not defined...Theorem:
The number of permutations of n dissimilar things taken r ..
The number of permutations of n dissimilar things taken r ..Arithmetic Mean (A.M.)
1. If a, x, b are in A.P, then x is called the arithmetic mean (A.M.) between the extremes a and b. 2. a. To insert n arithmetic means between two given quantities. Let a and b be any two given quantities, and let A 1 ,A 2 ,A 3 ,-----A n be n arithmetic means to be inserted between a and b so that ..
1. If a, x, b are in A.P, then x is called the arithmetic mean (A.M.) between the extremes a and b. 2. a. To insert n arithmetic means between two given quantities. Let a and b be any two given quantities, and let A 1 ,A 2 ,A 3 ,-----A n be n arithmetic means to be inserted between a and b so that ..Suggested answer:
Let S n = 1+2+3+4+...+n This series is an A.P. Here a=1, d=1, l = t n = n 2. To find the sum to squares of first n natural numbers. or..
Let S n = 1+2+3+4+...+n This series is an A.P. Here a=1, d=1, l = t n = n 2. To find the sum to squares of first n natural numbers. or..To find the sum to infinity of a GP when the common ratio r is numerically less than 1
Consider the GP a, ar, ar 2 ... ..
Consider the GP a, ar, ar 2 ... ..Some Properties of A.P.
If a,b,c,d are in A.P., then (ii) ka, kc, kb, kd are also in A.P. A remark on finding a few members of an A.P. whose sum is given along with other conditions: i) If the sum of three numbers in A.P. is given, take the numbers as a-d, a, a+..
If a,b,c,d are in A.P., then (ii) ka, kc, kb, kd are also in A.P. A remark on finding a few members of an A.P. whose sum is given along with other conditions: i) If the sum of three numbers in A.P. is given, take the numbers as a-d, a, a+..See what our Users say :
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