math integers multiplication of two integers

i) A sequence of multiples of 5 5, 10, 15, 20, ii) A sequence of reciprocals of positive integers The above two sequences are clearly the infinite sequence..

Question 1 - Question: Answer: As n represents all positive integers, we have Multiplying the above terms of both sides respectively, we get Multiplying both sides of inequality by n!, we g..

The same principle can be generalized to three or more events occurring in succession as follows: If n operations can be performed in m 1 ,m 2 ,m 3 ,...m n ways respectively, then all n operations in succession can be performed exactly in m 1 ,m 2 ,m 3 ,...m n ways. The above..

Factorial Notation - Let n be a positive integer. The continued product of first n natural numbers is called factorial n and is denoted as ..

Elementary transformations are of the following three types: Interchange of any two rows (or columns) The multiplication of the elements of a row (or column) by a non-zero number. The addition to the elements of any row (or column) the corresponding elements of any othe..

The inverse of a square matrix if it exists, is unique. Let A be an invertible square matrix. If possible, let B and C be two inverse of A. Then AB = BA = I. AC = CA = I (by def. of inverse) Now, B = BI = B(AC) = (BA)C [ Matrix multiplication is associative] = IC = C i.e., B =..

>If A, B and C are the matrices which can be multiplied then (a) Matrix multiplication is not commutative, i.e., AB BA (always) (b) Associative law holds good for matrix multiplication, i.e., (AB)C = A(BC) (c) Matrix multiplication is distributive with respect to addit..

What should be the sign of the integers, if the product of the two integers is positive? => Either both the integers should be positive or both negative. or Multiplier is positive and multiplicand is negative. or Multiplier is negative and multiplicand is pos..

The product of two consecutive even integers is 624. Find the integers. => even integers are not possible or - 26, - 24 or 24, 26 or - 26, -28 or 22, 24 or 120, 504..

x 2 - 2x - 48 = x 2 - 8x + 6x - 48 = x(x - 8) + 6(x - 8) = (x - 8) (x + 6) When the coefficient of the highest power is not unity. i.e., type ax 2 bx c, when and b and c are integers. Multiply (3x + 2) (x + 4) and consider t..