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Definition
Let R i denotes the i t h row of the matrix A = [a i j ] then the elementary row operations on the matrix A are defined as: 3. R i g R i + kR j means multiply each element of j t h row by k and add it to the corresponding elements of i t h row. The corresponding column tra..
Harmonic Mean (H.M.)
If three quantities are in harmonic progression, then the middle quantity is called the harmonic mean between the other tw..
Arithmetic Mean (A.M.)
If a, x, b are in A.P, then x is called the arithmetic mean (A.M.) between the extremes a and ..
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 ins..
To insert n Harmonic Means between two given quantities
Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and ..
To insert n Harmonic Means between two given quantities
Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and b. Let d = common difference of the A.P. Hence h 1 , h..
Note:
Strictly speaking 0! has no meaning. But since n P n = n! we may understand 0! = ..
Question 7
Question: How many three letter words (with or without meaning) can be formed out of the letters of the word LOGARITHMS if repetition of letters is not allowed? Answer: Number of letters in the word LOGARITHMS is 10. The three letter words formed by using these letters will be..
Sequences and Series Examples
1 , A 2 ,.....,A n are called the n arithmetic means between a and b. (vii) The sum of n A.M.s between given numbers a and b is equal to n times the A.M. between a and b. (viii) If a, b, c are in A.P., then for any k: (a) a+k, b+k, c+k are in A.P. (b) a-k, b-k, c-k a..
Definition of a Matrix
A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracket. Matrices are denoted by capital lette..
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