Consistency, inconsistency and number of solutions of a system of linear equations by examples, solving system of linear equations in two or three variables using the inverse of a matrix A linear equation multiple variables: x, y, z etc. is an equation of the form: ax + by + cz = p, where a, b, … Read more
Arithmetic Mean The A.M or the Arithmetic Mean is referred to as the average of 2 given numbers. And if one A.M “A” is included between the two numbers which are “a” & “b”, then A is called the arithmetic mean present in between the numbers, a & b. A.M. = A = $\frac{a+b}{2}$ Here, … Read more
Arithmetic and Geometric series infinite G.P. and its sum If there’s a sequence 10, 20, 30, 40, then each term is 10 more than the earlier term. This is the example of the (AP) Arithmetic Progression & a constant value which clearly describes the difference in between any 2 consecutive terms which is known as … Read more
Calculating averages for various series had been a part of most of the mathematics practices well, like the arithmetic mean, the geometric mean of series and sequences could be worthwhile calculations. Geometric Mean As the name suggests, the geometric mean formula is useful for calculating the geometric mean of a considerable set of numbers. Recall … Read more
There is absolutely much to know about series and sequences that may be effective for dealing with various events taking place in regular lives and other areas of professional working. Geometric Progression In a sequence of terms, if each term is observed to be a constant multiple of the preceding term, the sequence is then … Read more
If the sequence is geometric, then without really adding all the actual terms, there are methods for finding the sum of 1st n terms, which are denoted by Sₙ. With the use of the formula, you can find the sum of the first Sₙ terms of the geometric sequence Sn = a₁(1−rⁿ) / 1−r, r≠1 … Read more
You may have already been introduced to finding averages. Well, arithmetic mean is just that. Understanding Arithmetic Mean In general language, average data and arithmetic mean are synonymous. It could also be referred to as the representative value for a group of data. Suppose that you have been given n number of elements and required … Read more
Geometric Progression’s general term with “a” as the first term and “r” as the common ratio is defined by: aₙ = a.rⁿ⁻¹ Where ‘n’ = the number of terms. Theorem: To prove that G.P.’s nth term with “a” as the first term & “r” as the common ratio which is given by: aₙ = a.rⁿ⁻¹ … Read more
The binomial theorem or the binomial expansion is loaded with its extremely large applications and is immensely beneficial in the simplification of the lengthy calculations. The binomial theorem or the expansion for the nth polynomial degree is given by: If there’s a need for the computation of (1+x)¹² which doesn’t mean that you to multiply … Read more
Recall that a cofactor matrix C of a matrix A is the square matrix of the same order as A in which each element aij is replaced by its cofactor cij . The adjoint matrix of [A] is written as Adj[A] and it can be obtained by obtaining the transpose of the cofactor matrix of … Read more