Learn Gaussian Elimination

Introduction to learn Gaussian elimination:

In linear algebra, Learning Gaussian elimination is an algorithm for solving systems of linear equations, finding the rank of a matrix, and calculating the inverse of an invertible square matrix. Gaussian elimination is named after German mathematician and scientist Carl Friedrich Gauss.

Elementary row operations are used to reduce a matrix to row echelon form. Gauss–Jordan elimination, an extension of this algorithm, reduces the matrix further to reduced row echelon form. Gaussian elimination alone is sufficient for many applications.

I like to share this Gaussian Standard Deviation with you all through my article.

Solving by Learning Gaussian Elimination:


A technique of solve a method of n linear equations in a n unknowns, in which there are first n - 1 steps, the math step of which consists of subtracting a lots of the math equation from both of the pursue ones so as to remove one variable, ensuing in a triangular set of equations which can be solved by turn around substitution, compute the nth variable from the nth equation, the (n-1)st variable from the (n-1)st equation.

Understanding algebra formula chart is always challenging for me but thanks to all math help websites to help me out.

Example problems for learning Gaussian Elimination:


Example problems for learning Gaussian Elimination are as follows:

1) Solve the following system equation using Gaussian Elimination method.

3x + y = 9

3x – y = 15

Solution:

If add down, the y determination cancel out. So sketch an "equals" bar below the system, and add down:

3x + y = 9

3x – y = 15

--------------

6x = 24

x = 24 / 6

x = 4

At the present divide from side to side to solve for x = 4, and then back-solve, using either of the original equations, to find the value of y. The first equation have lesser facts, so back - explain in that one:

2(4) + y = 10

8 + y = 10

y = 2

Then the solution is (x, y) = (4, 2)

2) Solve the following system using Elimination method.

2x + 2y = 4 --- (1)

4x – 3y = 8 ---- (2)

Solution:

Multiply equation 1 with (3) and multiply equation, 2 with (2)

6x + 6y = 12

8x – 6y = 16

----------------

14x = 28

x = 28/14

x = 2

Apply x=2 in equation (1)

2(2) +2 y = 4

4 + 2y = 4

2y = 4 -4

y=0

Then the solution is (x, y) = (2, 0).

The World of Math

Introduction to world math :

In this article we are going to discuss about world math  Now a days math is one of the widely used part in the world. Sometimes math will challenge to solve the problems but every math has a solution to prove it. Let we see some math challenge problems to world math.

Please express your views of this topic Define Numerical Expression by commenting on blog.

Example Problems for math problems:


world math problem 1

Find the value for x in the expression `x/8` +x-`4/8` =0

Solution:

The given expression is `x/8` +x-`4/8` =0

We need to find the value of x

`x/8` +`(8x-4)/8` =0

The above expression can be written has

`x/8` +`(8x)/8` -`4/8` =0

Now add `4/8` on both sides of above equation

`x/8` +`(8x)/8` - `4/8` +`4/8` =`(0+ 4)/8`

`x/8` +`(8x)/8` =`4/8`

`(9x)/8` =`4/8`

Multiply by 8 on both sides of above equation

`(9x)/(8)xx(8)=` `4/8 xx8`

9x=4

Now divide by 9 on both side of the above

x=`4/9`

world math problem 2

Multiply the fraction `120/65` and `148/96`

Solution:-

Given we need to multiply fractions`120/65` and `148/96`

Fractions must multiplied using the formula `(axxc)/(bxxd).`

Here a = 120, b =65, c= 148, d=96

= `(axxc)/(bxxd).` =`(120xx148)/(65xx96) ` by solving it we get

A =`17760/6240`

= `37/13`

world math problem 3

Find the area of the circle with radius 54 feet. Important use symbol pie value approximately as 3.14

Solution:

We know that area of circle is equal to `pi` r2

Here the given radius is 54

Substitute the r value in the formula

=3.14x 542

=3.14x 54x 54

=9156.24

Therefore the area of circle is 9156.24 feet square

world math problem 4

Fine the surface area of cube in kilometers for the side is 30 m

Solution:

Area of cube A=6 * 302

A=6 *900

A=5400sq meters

1 square meter = 0.000001 square kilometer

5400 square meter = 5400 * 0.000001  = 0.0054

now surface area in kilometer is 0.005400 sq kilometers


Few More Example Problems for math problems


world math problems 5

Subtract the two fractions `32/15` and `94/15`

Solution:

The two given fractions are`32/15` and `94/15`

Step1: The given two fractions

`32/15` - `94/15`

Step2: Now we need to find the differences of `32/15` and `94/15`

`(32-94)/15`

Step3: The difference of 32 and 94 is -62

=-`62/15`

world math problem 6

Find equivalent fraction `7333/336`

Solution:

Equivalent fraction has to multiply numerator and denominator by same number

Denominator is 336 and the numerator is 7333

Multiply the denominator and numerator by 160

= `(7333xx160)/(336xx160)`

= `1173280/53760`

So the equivalent fraction is `7333/336` is` 1173280/53760`

Learn to Read a Ruler

Introduction of learn to read a ruler:

Math can understand through various equipment. The ruler is one of the main basic equipment for math. In every math problems the ruler plays a role to compute the answers. The ruler is measurable equipment for math. Ruler learns has two measures with cm in one side and mm in another end. Using the two measures we can have the two types of measuring terms.

Please express your views of this topic Indirect Measurement by commenting on blog.

Learn to read a ruler:


The ruler is a measuring tool. The origin of the measuring tool is made from the man’s foot. To find the area’s measurement the man is asked to cross through the area for measuring the area’s measurement. The measure read in the yard can be done through the average man’s normal foot steps. Make the both measures to view, they won’t be exact. Till now the horses are made to measures in hands. This idea shows the origin of the ruler. We can have measuring idea with the ruler through the project on measuring the classroom. The classroom can be measured with the ruler that makes a measure which can be noted through the read that given over the scale. The measures about the book can be made along the measures with the scale.


More Learning to read a ruler:


Hence the learn of ruler can made to have the measures in the two ways. The first way is in the centimeters and the second way is in millimeters. The ruler is the simple measuring tool which is meant for measuring. Ruler is made to have in the way which gives the various changes that makes measures. The measure in the yard can be done through the average man’s normal foot steps. Make the both measures to view, they won’t be exact. Till now the horses are made to measures in hands. This idea shows the origin of the ruler.

Learning Support Math

Introduction for math learning support:

Math support learning  is a most interesting subject comparing to other subjects.It is the lesson for learning support math patterns, numbers, and shapes. Basic concepts of math are  Addition (a + b), subtraction (a-b), multiplication (a*b) and division (a/b) a and b are the numbers or integers. In this article, we are going to see some solved math support learning. I like to share this list of the prime numbers with you all through my article.


Example Problems for math problems:


Learning for support math problem 1:

Perform the Plus operation for 300 and 584

Solution:

Given we need to find the sum of 300 and 584

300

584  (+)

----------------

884

--------------

So the answer for 300 and 584 is 884

Learning for support math problem 2:

Multiplying two numbers 168 and 43

Solution:

The given two numbers 168 and 43

We need to find the product of two numbers

By Multiplying  168 and 43

168 × 43

--------------------

5    0  4

6  7   2

--------------

7  2   2  4

--------------

We get  7  2   2  4

Learning for support math problem 3:

Find equivalent fraction `166/65`

Solution:

Equivalent fraction has to multiply numerator and denominator by same number

Denominator is 65 and the numerator is 166

Multiply the denominator and numerator by 24

= ` (166xx24)/(65xx24)`

=`3984/1560`

So the equivalent fraction is `166/65` is  `3984/1560`

Learning for support math problem 4.

Subtract the two fractions `174/112` and `224/112`

Solution:

The two given fractions are `174/112` and `224/112`

Step1: The given two fractions

`174/112` - `224/112`

Step2: Now we need to find the differences of   `174/112` and `224/112`

`(174-224)/112`

Step3: The difference of 174 and 224 is 50

= - `50/112`

Understanding formula to find percentage is always challenging for me but thanks to all math help websites to help me out.

Few More Example Problems for math problems


Learning for support math problem 5:

Round the number 136 to the nearest 10

Solution:

The given number is 136

The number in 10 places is 3 and the number 1s places is 6

Since the number ten places is 6 so we make the number 6 as zero and we add 1 to 3

So the number 136 grounded to nearest 10 becomes  140

Learning for support math problem 6:

Identify 135 is a prime number or not

Solution:

The given number is 135

We need to identify prime number or not

To identify 135  is a prime number we need to determine in factors

Factors of 135  are 1  3  5  9  15  27  45  135

The number to be a prime number it must have only two factors 1 and itself

So here 135  has eight factors so it is not a prime number

Math 1010 Answers

Introduction to Math 1010 Answers:

In mathematics, numeration is one of the main sources describing about numerals such as number system. The number is also used for abstract object and symbolic representations of numbers. There is addition, multiplication, division, subtraction operation in math. The common usage of math is to solve the problem and finding the solution. The given problem can be performed by any one of the above operation. Let us see about math 1010 answers in this article.

Please express your views of this topic Row Operations by commenting on blog.

Example Problems for Math 1010 Answers


Using Addition Operation in Math

Example 1:

Add 1000 and 10?

Solution:

Let us add the given problem.

Write the given whole number 1000 first and then write the given whole number 10 second one by one.

1000 (addend)

(+)   10 (addend)

--------------

1010

--------------

The sum for adding 1000 and 10 is 1010.

Using Subtraction Operation in Math

Example 2:

Subtract 2220 and 1210?

Solution:

Let us subtract the given problem.

Write the given whole number 2220 first and then write the given whole number 1210 second one by one.

2220 (minuend)

(-) 1210 (subtrahend)

--------------

1010 (difference)

---------------

The difference for subtracting 2220 and 1210 is 1010.

Using Multiplication Operation in Math

Example 3:

Multiply 101 and 10?

Solution:

Let us write the given problem as in the below form. Here, 101 is multiplicand and 10 is multiplier.

101 ×

10

----------------

1010

----------------

The product for multiplying 101 × 10 is 1010.

Using Division Operation in Math

Example 4:

Divide 9090 by 9?

Solution:

Let us write the given problem is in form of 9090 ÷ 9 and put the divisor on the left side of the division bracket and dividend on the right side of the division bracket.

Check whether the 9 goes into 9. The number 9 should go into 9 for 1 time. Continue with the division method.

9)9090(1010

9

----------------

009

009

----------------

00

-----------------

The quotient for dividing 9090 by 9 is 1010.


Practice Problems for Math 1010 Answers


1. Add 990 and 20.

Answer: 1010

2. Subtract 4880 and 3870.

Answer: 1010

3. Multiply 220 and 5.

Answer: 1010

4. Divide 7070 by 7.

Answer: 1010

How to do Sets in Math

Introduction to do sets in math:

A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics. Set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. Let us see about the concept of how to do sets in math. (Source: Wikipedia)

Please express your views of this topic Set Theory Union by commenting on blog.

Sets in math:


By using two methods we can do the sets in math. They are,

Roster or tabular form
Set-builder form
How to do sets in math by using Roster form:

The elements are separated by using the commas, and the elements are placed inside of braces { }. For example, the set of all odd positive integers less than 8 is expressed in roster form as {1, 3, 5, 7}.

How to do sets in math by using Set-builder form:

For example, in the set {1, 3, 5, 7, 11}, all the elements possess a common property, namely, all are prime number, which are not possessed in any other set. Representing this set by P, we write P = {x: x is a prime numbers in real numbers}


Example problem in set:


Problem1: Find the solution set of the following equation by using roster form x 2 + x – 2 = 0.

Solution:

x 2 + x – 2 = 0 can be expressed as (x – 1) (x + 2) = 0, that is x = 1, – 2.

Therefore, the solution is {1, – 2}.

Problem 2: Find the set {x: x is a positive integer and x2 < 30} in the roster form.

Solution:

By the given we need the following numbers to represent the set -1, 2, 3, 4, 5.

So, the given set in the roster form is {1, 2, 3, 4, 5}.

Problem 3: Find the set A = {1, 4, 9, 16, 25 . . .} by using set-builder form.

Solution:

We may write the set A as A = {x: x is the square of a natural number}

Alternatively, we can write A = {x: x = n2, where n ∈ N}

In this section we have seen about the concept of how to do sets in math.

Mixed Numbers in Math

Introduction to mixed numbers in math:

In math, Mixed number is very important study.  We will study mixed numbers under algebra in math. This is very helpful when using fractions in math

Mixed number is a one form of fraction.  Mixed number is also known as mixed fraction. Mixed number will get by converting improper fraction into mixed fraction.

Mixed number includes an integer then a proper fraction.  The example of mixed numbers are 1 `2/3` , 5 `7/8` , - 1 `6/5` .

For example, convert an improper fraction into mixed number.

`4/3` = 1 `1/3` .

Let us see sample problems involving mixed numbers in math.

Having problem with Find Inverse Function keep reading my upcoming posts, i will try to help you.

Example Problems on Mixed numbers in Math:


Problem 1:

Subtract  `1/2` from 4 `1/2` .

Solution:

First, we need to convert mixed number into improper fraction.  The steps are following,

4 `1/2`

Multiply the denominator by an integer.

4 x 2 = 8

Add that number with numerator.

8 + 1 = 9

Now write the result in the numerator and keep the denominator same.

4 `1/2`  = `9/2`

Now rewrite the operation.

`9/2` – `1/2`

Here the denominator is same in both fractions. So we just subtract numerators and keep the denominator same.

`(9-1)/2` = `8/2` = 4 .

The answer is 4.

Problem 2:

Subtract  - 2 `3/5` from - 1 `3/5` .

Solution:

First, we need to convert mixed number into improper fraction.  The steps are following,

-2  `3/5`

Multiply the denominator by an integer.

2  x 5 = 10

Add that number with numerator.

10 + 3 = 13

Now write the result in the numerator and keep the denominator same.

-2 ` 3/5`  = - `13/5`

Now we need to do same process for another mixed number.

-1 `3/5`

Multiply the denominator by an integer.

1  x 5 = 5

Add that number with numerator.

5 + 3 = 8

Now write the result in the numerator and keep the denominator same.

-1 ` 3/5`  = - `8/5`

Now rewrite the operation.

-1 `3/5` – (- 2 `3/5` ) = -` 8/5` – (-`13/5` )

= - `8/5` + `13/5`

= `13/5` – `8/5`

Here the denominator is same in both fractions. So we just subtract numerators and keep the denominator same.

`(13-8)/5` = `5/5` = 1 .

The answer is 1.

Problem 3:

Multiply the mixed numbers:  -2 `2/3` and  4 `1/10`

Solution:

First, we need to convert mixed number into improper fraction.  The steps are following,

-2 ` 2/3 `

Multiply the denominator by an integer.

2  x 3 = 6

Add that number with numerator.

6 + 2 = 8

Now write the result in the numerator and keep the denominator same.

-2  `2/3`  = - `8/3`

Now we need to do same process for another mixed number.

4 `1/10`

Multiply the denominator by an integer.

4  x 10 = 40

Add that number with numerator.

40 + 1 = 41

Now write the result in the numerator and keep the denominator same.

4 `1/10`  = `41/10`

Now rewrite the operation.

-2` 2/3` x 4` 1/10` = - `8/3` x `41/10`

= - `328/30`

=` -164/15`

= - 10 `14/15`

Understanding hard math problems with answers is always challenging for me but thanks to all math help websites to help me out.

Practice Problems on Mixed numbers in math:


Problem 1:

Find the solution of  -2 `1/5` and -1 `3/4`

Answer:

3 `17/20`

Problem 2:

Find the solution of – 2 `7/8` + 4 `3/8`

Answer:

1 `1/2` .

Problem 3:

Find the solution of `1/6` – 1 `5/6`

Answer:

-1 `2/3`