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Introduction to Matrix & Factors in Math’s

An array or rectangular arrangement of numbers in rows and columns is known as a matrix. Or we can say that when some expressions are arranged in rows and columns while being surrounded by square brackets on both sides it is called a matrix.

Definition of Matrices

However, to exactly define a matrix, we would say, a matrix is a rectangular arrangement of expressions, numbers, or symbols. In which the arrangement of elements is done in vertical columns and horizontal rows.

Dimension of Matrices

The entries or elements in vertical arrangement are known as columns while the horizontal placements are known as rows. The size of a matrix is determined by the number of rows and columns which we call as the dimension of the matrix. 

The dimension of a matrix is most commonly known as order of a matrix, while writing order of a matrix firstly the rows are represented and then comes the columns. A matrix may have one or more than one number of rows and columns. For instance, a matrix having 4 rows and 2 columns is represented as 4 x 2

Element of matrices

Any entry or expression with the matrix bracket is known as the matrix element. By naming the columns and rows in which a specific element is present we can successfully identify that element in the matrix.

Notation of matrices

Each pair of rows and columns in a matrix represents an equation forming the elements in a 3D space. Matrices are specifically represented by capital letters e.g. A, B or C while the elements or entries within a matrix are represented by lowercase letters having a subscript of row and column.

Types of Matrices

Based on the order of a matrix and several other properties, the matrices are differentiated into following types:

Row matrix

If a matrix has no column in it and only one row, then it is known as a row matrix.

Column matrix

In the same way, if a matrix has no row and has only one column in it, then it is called a column matrix.

Square matrix

A matrix in which the number of columns is equal to the number of rows is a square matrix. Alike to Square a matrix having equal rows and columns is termed as a square matrix.

Rectangular matrix

Contrary to the square matrix, if the columns and rows in a matrix are not equal in number then the matrix is called a rectangular matrix.

Diagonal Matrix

If all the diagonals of a square matrix are zero, the matrix is known as a diagonal matrix. For a square matrix to be diagonal also, having zeroes in all its diagonal is a compulsion.

Scalar matrix

If all the elements of the diagonal matrix in its diagonals are equal to any non-zero constant, then it is termed as a scalar matrix. In other words, a scalar matrix is the diagonal matrix whose diagonal matrices are equal.

Zero or null matrix

A matrix with zero elements inside it is a null or zero matrix.

Identity or unit matrix 

In a scalar matrix if all the diagonal elements are 1 while all non-diagonal elements are 0 it is known as a unit or identity matrix.

Addition or Subtraction of matrices

The subtraction and addition of two matrices can occur only if that matrix has the same number of rows and columns in it, or you can say that if a matrix has the same dimension. After having the same dimension, we can subtract or add by simply adding or subtracting the entries at the same spot or the corresponding entries. 

Multiplication of matrix

The procedure of multiplying the matrices is not as easy and simple as adding and subtracting matrices. All you have to do is multiply the rows of the first matrix with the columns of the second matrix. After multiplying across the rows and columns, add the products you get after multiplying, the results you receive after adding the products is the new matrix. The online tool used for the multiplication of matrix is called matrix multiplication calculator.

Likewise, during the addition and subtraction of matrices, you have to consider the rows and columns are equal in number. In the same manner for multiplication between two matrices, you have to consider if the rows of the first matrix are equal in number to the columns of the second matrix.

What is a Factor?

Factors are in general those numbers that are fully or accurately divided by the original number. The factors are generally whole numbers that are used to divide any greater number than itself equally.

On account of a prime number (the number that is just separable without help from anyone else). It will have only two factors, for example, 1 and number itself. Then again, any composite number, including s prime factors, will have multiple factors. It suggests, observing at least two numbers esteems, the result of which being equivalent to the underlying amount is the thing known as a variable.

For finding a typical variable, as a matter of first importance, the most widely recognized monomial factor (figuring out normal terms) of each term is distinguished, and afterward the first polynomial is separated by this, with the end goal that the subsequent element is acquired. The second variable in factorization anyway is a polynomial all of the time.

Related: You may also like to read the Top 7 Tips You Must Consider To Make Your Math Homework

How to Calculate Factor?

The most simplest method to calculate each and every factor of any number is to use the prime factorization method with the help of the division method. According to the prime factorization method, you need to divide the divisor by the smallest possible integer that can divide it. Later on, continue dividing by that integer until it can’t further divide.

For example, we take the smallest integer “2”. Then we will continue divide number until it will no more dividable by “2”. Then we change our integrer by some greater possible number e.g 3,4,5 etc.

The common steps that we have to follow in prime factorization method is given as follow:

  1. Divide by Smallest Number
  2. Continue Division
  3. Change Divisor
  4. Got Factors

But Beside to these steps, There are numerous online factoring calculator with steps available that provide us all possible factors against any divisor number.

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