Elementary Operation (Transformation) of a Matrix

I will help you understand the major three operations on Elementary Operation (Transformation) of a Matrix.

There are six operations (transformations) on a matrix, three of which are due to rows
and three due to columns, which are known as elementary operations or
transformations.

(i) The interchange of any two rows or two columns is an elementary operation. Symbolically the interchange of ith and jth rows is denoted by Ri ↔ Rj and interchange of ith and jth column is
denoted by Ci ↔ Cj. Solving matrices can be simplified with these operations.

(ii) The multiplication of the elements of any row or column by a non zero
number is another operation. Symbolically, the multiplication of each element of the ith row by k,
where k ≠ 0 is denoted by Ri → k Ri. The corresponding column operation is denoted by Ci →kCi

(iii) The addition to the elements of any row or column, the corresponding
elements of any other row or column multiplied by any non zero number.
Symbolically, the addition to the elements of ith row, the corresponding elements
of jth row multiplied by k is denoted by Ri → Ri + kRj.

These operations are used in solving matrices.

How to Solve Matrices Problems

I am showing a few Solved Matrices Problems
Problem - 1 - If a matrix has 8 elements, what are the possible orders it can have?
Solution - We know that if a matrix is of order m × n, it has mn elements. Thus, to find all possible orders of a matrix with 8 elements, we will find all ordered pairs of natural numbers, whose product is 8. Thus, all possible ordered pairs are (1, 8), (8, 1), (4, 2), (2, 4) Hence, possible orders are 1 × 8, 8 ×1, 4 × 2, 2 × 4
Problem 2 - Consider the following information regarding the number of men and women workers in three factories I, II and III

Men workers Women workers

I 30 25

II 25 31

III 27 26

Represent the above information in the form of a 3 × 2 matrix. What does the entry

in the third row and second column represent?

Solution -
The information is represented in the form of a 3 × 2 matrix as follows: The entry in the third row and second column represents the number of women
workers in factory III.

Will be back with more matrices problems

Types of Matrices

What is Matrics?

A matrix is an arrangement of items into labeled rows and columns within a table.

It shows the relationship between two categories of features that are relevant to the items in the matrix. The row headings represent features belonging to one category. The column headings represent features belonging to another category.

Types of Matrices:- Following are the types of Matrices

• Column matrix
• Row matrix
• Square matrix
• Diagonal matrix
• Scalar matrix
• Identity matrix
• Zero matrix

7th grade math equations

7th grade math equations are the basic introduction for students for quadratic equations.

An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent). Equations are written with an equal sign, as in the following problem

This algebra tutoring problem explain you more clearly about ,how to form an equation and get the answer for word problems.

Question:-

john traveled 234 miles in 14 days.His trip is for 42 days .Find the number of miles that he can travel in 42 days.


Answer:-

Miles:-  234    x


Days:-   14    42

Unknown quantity is taken as x.

Let's use a technique of cross multiplication from multiplication.com
By cross multiplication,we get

14 x = 234*42

divide by 14 on both sides

we get x=702

So john will travel 702 miles in total 42 days.

Types of angles

Topic:- Angles

In geometry and trigonometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle .

There are total 5 types of angles.

1. Acute Angle : an angle that is less than 90°, is called as acute angle.
2. Obtuse Angle:an angle that is greater than 90° but less than 180°
3. Right Angle :an angle that is 90° exactly , is called as right angle.Right angle triangle means an angle of a triangle should be 90°.
4. Straight Angle:an angle that is 180° exactly
5. Reflex Angle : an angle that is greater than 180°

We can recognize the angle in the following picture.
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Multiplication and division of fractions

Multiplication 
In general, when we multiply fractions, we multiply
the two numerators (the top numbers) to make the new
numerator, and multiply the two denominators to make
the new denominator.
For example:

7       4  
---- * -----
5       3


  7 * 4  
= --------
  5 * 3

   28
=  -------
   15


Division


7       4  
---- / -----
5       3

We can change this to multiplication by
simply changing the second fraction like,

7       3  
---- * -----
5       4


  7 * 3  
= --------
  5 * 4

    21
=  -------
    20

a word problem on finding the area

Topic:- Finding Area

Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a rectangle. Area is an important invariant in the differential geometry of surfaces

Question: -

The width of a swimming pool is 10 meters and
length is 30 meters. Then find the area of the
pool.

Solution:-

This geometry help ,will give you the solution of above question.

width of thepool = 10 meters

length of the pool = 30 m

Area of the pool = Area of the rectangle ( as the pool is in the shape of a rectangle) Length

x breadth = 10 x 30

= 300 square meters

So the area of the pool is 300 square meters


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