Summary
(iii) If 'a' and 'd' be the first term and common difference of the A.P. {T n }, then the sum of first n terms, S n is given by The form (a) is used when common difference 'd' is known and the form (b) is used when the last term 'l' is known. (iv) T 1 = S 1 a..
(iii) If 'a' and 'd' be the first term and common difference of the A.P. {T n }, then the sum of first n terms, S n is given by The form (a) is used when common difference 'd' is known and the form (b) is used when the last term 'l' is known. (iv) T 1 = S 1 a..Some important results
or This property is known as COMPONENDO & DIVIDENDO. (6) If , then each of these ratios equals where l,m,n are real numbers. L..
or This property is known as COMPONENDO & DIVIDENDO. (6) If , then each of these ratios equals where l,m,n are real numbers. L..Arithmetic Mean (A.M.)
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..
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..Note 1:
The L.H.S of (ii) and (iii) will have only finite number of terms, because n C r = 0 in case r>n..
Null Matrix or Zero Matrix
A matrix of order m x n whose elements are all 0 is called a null matrix (or zero matrix) of order m x n. It is usually denoted by O or more clearly [O] m , n..
Principle of Mathematical Induction
If P(n) is a statement (n N); such that 1. P(1) is true and 2. truth of P(k) implies the truth of P(k+1), then by the principle of mathematical induction (P.M.I.), the statement P(n) is true for n N..
Summary
A matrix is defined as a rectangular array of elements. If the arrangement has m rows and n columns, then the matrix is of order mxn (read as m by n). A matrix is enclosed by a pair of parameters such as ( ) or [ ]. It is denoted by a capital lette..
Principle of Mathematical Induction
If P(n) is a statement (n N); such that: P(1) is true and truth of P(k) implies the truth of P(k+1), then by the principle of mathematical induction (P.M.I.), the statement P(n) is true for n N..
If P(n) is a statement (n N); such that: P(1) is true and truth of P(k) implies the truth of P(k+1), then by the principle of mathematical induction (P.M.I.), the statement P(n) is true for n N..Definition of Matrix
It is a rectangular array of numbers, arranged in rows and columns. The number of rows (say m) and the number of columns (say n) determine the order of the matrix. It is written as m x n (to be read as m by n..
Multiplication of a matrix by a scalar
Let A=[a i j ] be an m x n matrix and k be any number called a scalar. Then the matrix obtained by multiplying every element of A by k is called the scalar multiple of A by k and is denoted by kA. Thus, kA = [k a i j ] m x n..
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