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An important note:
If the product of three numbers in GP is given, take the term as a/r, a, ar. But if the product of the numbers is not given, the terms are in the ordinary for..
Factorial Notation
Factorial Notation - Let n be a positive integer. The continued product of first n natural numbers is called factorial n and is denoted as ..
Properties of Transpose
(A T ) T = A (A + B) T = A T + B T , A and B being of the same order. (KA) T = KA T , k be any scalar (real or complex) (AB) T = B T A T ; A and B being conformable for the product A..
Properties of Determinants
If the rows and columns of a determinant are inter-changed, the value remains unaltered. If any two rows (columns) of a determinant are identical, its value of the determinant is zero. If any two rows (columns) of a determinant are interchanged, the value of the determinant is (-1) times th..
If the rows and columns of a determinant are inter-changed, the value remains unaltered. If any two rows (columns) of a determinant are identical, its value of the determinant is zero. If any two rows (columns) of a determinant are interchanged, the value of the determinant is (-1) times th..Summary
>These formulae are used when 'last term' is given. (v) If 'a' and 'r' be the first term and common ratio of a G.P. such (vi) If the sequence a, G 1 , G 2 ,....,G n , b of positive numbers is a G.P., then the numbers G 1 , G 2 ,....,G n , are called the n geometric means between a and b. (vii) The ..
>These formulae are used when 'last term' is given. (v) If 'a' and 'r' be the first term and common ratio of a G.P. such (vi) If the sequence a, G 1 , G 2 ,....,G n , b of positive numbers is a G.P., then the numbers G 1 , G 2 ,....,G n , are called the n geometric means between a and b. (vii) The ..Cartesian Product
Given two sets A and B. Then, all possible ordered pairs (x, y) obtained such that and is called the Cartesian product of the sets A and ..
Given two sets A and B. Then, all possible ordered pairs (x, y) obtained such that and is called the Cartesian product of the sets A and ..Ordered pairs and Cartesian products
Ordered pairs and Cartesian products - An ordered pair is a pair of entries in the specific order. The two entries are separated by comma and enclosed within brackets. An ordered pair is a pair of entries in the specific order. The two entries are separated by comma and enclosed..
Ordered pairs and Cartesian products - An ordered pair is a pair of entries in the specific order. The two entries are separated by comma and enclosed within brackets. An ordered pair is a pair of entries in the specific order. The two entries are separated by comma and enclosed..All about Relation and Cartesian Product
Summary Ordered Pairs and Cartesian Product - An ordered pair has a pair of elements which occur in a definite order. An ordered pair has a pair of elements which occur in a definite order. Cartesian Product - Given two sets A and B, all possible ordered pair..
Cartesian product of two sets
Let A and B be two non-empty sets, then the cartesian product of A and B denoted by A x B = {(a, b) | a A, b B..
Ordered pairs and Cartesian products
An ordered pair is a pair of entries in the specific order. The two entries are separated by comma and enclosed within bracket..
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