Different types of Matrices

Matrix is a rectangular array of numbers or functions which are called the elements or the entries of the matrix. The elements or entries are arranged in rows and columns in either () or [] brackets. The elements of a matrix are denoted by aij where ‘i’ is the row number and ‘j’ is the column number. We can only add or subtract two matrices if they both have same number of rows and columns.

Order of matrices: An order of the matrices is written as m X n where m is the number of rows and n is the number of columns in it. That means a matrix of order 2 X 2 can only be added to a matrix of order 2 X 2 and a matrix of order 3 X 3 can only be subtracted from a matrix of order 3 x 3.

Types of matrices

1. Column matrix: A matrix is said to be a column matrix if has only one column. For example: - a matrix of order 4 X 1 is said to be a column matrix as it has four rows but only one column. In general, a matrix of order m X 1 is considered as column matrix where m can be any real number.
2. Row matrix: A matrix is said to be row matrix if it has only one row. For example: - a matrix of order 1 X 4 is said to be a row matrix as it has four columns but only one row. In general, a matrix of order 1 X n is considered as row matrix where n can be any real number. A example of row matrix is [2 , 6, 11, 7].
3. Zero matrix: A matrix is said to be zero matrix if all its elements or entries are zero. It is also called a null matrix. For example: - [0], [0 0] are zero matrices. We denote zero matrix by O.
4. Square matrix: A matrix is said to be square matrix if its number of rows are equal to number of columns. Thus m X n is a square matrix if m = n and is known as a square matrix of order ‘n’.
5. Unit matrix: A matrix is said to be unit matrix if all its elements or entries are one. For example: -
[1], [1 1], [1 1 1] are all unit matrices.

Polynomial Factoring

Factoring polynomial is similar to factoring numbers, but you will be dealing with expressions instead of numbers. In order to factor a polynomial, you have to determine the polynomial that divides the original polynomial evenly.

Polynomial Factoring

How to factor a polynomial?
Different approaches are used to factor the polynomial; most common approaches are simple factoring, and factoring in pairs. In this article, you will find examples for these two approaches of polynomial factoring.

Simple Factoring
In simple factoring, you identify a common factor for the expression and place it before the parenthesis. What is a common factor? To know that, look at the example below:
5x + 60 = 5 (x) + 5(6) = 5 (x+12)

Now the common factor of the above expression is 5. To cross verify, multiply the factor with each term in the expression and ensure if you are getting the original polynomial back. For example,

5(x+6) = 5 multiplied with x + 5 multiplied with 12 = 5x + 60 (the original polynomial)

Factoring in Pairs
“Factoring in Pairs” is yet another factoring polynomials solver. This approach is used when you cannot find any common factor for the terms in the expression. In this approach, the expression is split into pairs of terms and then each pair will be factored separately. Here is an example:

Find the factors of ab-5b-2a+10.

This polynomial algebraic expression includes 2 variables namely a and b. There is no common factor for these 4 terms. In this case, take the first two terms and find a common factor. Similarly, take the last 2 terms and find a common factor, as shown below:

ab-5b-2a+10 = b (a-5) -2 (a-5) = (b-2) (a-5)

In the above step, the first two terms ab-5b are taken into consideration. Take the common factor out, it is b. Now it becomes b (a-5). Similarly take the next two terms -2a+10. The common factor is 2 here. When you put it as -2, the expression becomes -2 (a-5). Now the expression can be further simplified as (b-2) (a-5).

If the consecutive terms do not have any common factors, then you can rearrange the terms based on the commonality and then do the factoring.

Rounding Decimals

Let's learn about rounding decimals in today's post.

Rounding decimals is nothing but turning a number to the nearest tens, hundreds, thousands or so on. Suppose we are adding a decimals and the answer we get is 4.6, here we can round the decimal to 5. If the number after decimal is 5 or more than 5, it can be rounded by adding 1 and if it is less than 5, it can be rounded by removing the decimal value. This method is the method of rounding decimals.

Next time i will help you with the concept of decimals number line.

statistics independent events

Independents Events is a key word often referred to in probability calculations. Knowingly or unknowingly , they use Independents Events often in the theory and application of probability. events are independent events, if the occurrence of event does not affect the probability of other variables. i.e.., positive or negative.

Algebra Solver

algebra solver step by step:

Algebra is one of the a lot of basal aspect of mathematics in which, we about-face from basal accession to variables. Algebra has assorted subdivisions like polynomials, graphing, arrangement of equations, logarithms, etc. Polynomial is aswell a allotment of algebra. Expressions of an exact ambit end to end with variables (x, y) and constants are alleged as polynomials. Polynomials absorb with operations like accession and subtraction. Algebra footfall by footfall solver can be acclimated for ths affectionate of problems. The algbra footfall by footfall solver solves the expressions accustomed in it with footfall by footfall explanation. The afterward sections shows the footfall by footfall solver free.

Mean

Mean Deviation:
What are the Merits of Beggarly Deviation:
1. Beggarly aberration is acclimated in added fields aswell for archetype business, and economics.
2. It is calmly to acquisition out the median.
3. Based on the deviations, it gives the bigger measurement.
4. The capital focus point is to any admeasurement acclimated for statistical Analysis
What are the Demerits of Beggarly Deviation:
1. The boilerplate atom mean. it is difficult to abridge the beggarly deviation.
2. It is not simple to account for added ambit X, M.
3. Beggarly aberration and its co able taken from X, M and Z.
4. In case ambit increases, and the sample increases, the boilerplate aberration aswell increases.
We had advised what is beggarly deviation.
5. Here absolute and abrogating assurance are neglected.

Algebra Expresions

Algebra Expressions
Intermediate algebra problem: 2
Solve: 7x - 5 = 79
Solution:
Given: 7x – 5 =79
7x=79 +5
7x=84
x=84 * 1/7
x=12