Thursday, June 13, 2024

Application Of Linear Algebra In Daily Life

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A Deliciously Simple Application Of Algebra In Real Life

Real Life Applications Of Linear Equations | Applications of Linear Equations in Real Life

Imagine that youre going to a big holiday feast, and youre in charge of buying the groceries and cooking the meal. You have decided that the main course for the meal will be a nice juicy turkey. As you look around the supermarket to choose a turkey, you are disappointed to find only one remains.

The weight on the package says that the turkey weighs 18 lbs. How can you determine how many people this turkey will feed so that nobody goes hungry at dinner?

As a general rule of thumb, you need approximately 1.5 lbs of turkey for each person. You pull out a piece of paper and a pen and write down the following algebraic equation:

What you have just performed is one of the most basic, real-life uses for algebra. A variable value, x, represents the number of people who can be fed with an 18 pound turkey if we assume that 1.5 lbs are needed for each person. In this case, we have solved for x to determine that our 18 pound turkey can feed a total of 12 people.

While this example may seem trivial, it illustrates that we often use algebra without realizing it. Thanks to experience, we often do these quick computations in our heads, but at the root of what we are solving is an algebraic equation. Now, look ahead to the next part of our holiday dinner preparation for another application of algebra that you can use in real life.

What Are The Applications Of Linear Equations In Real Life

In real-life situations where there is an unknown quantity or identity, the use of linear equations comes into play, for example, figuring out income over time, calculating mileage rates, or predicting profit. Most of the time mental calculations are used in some real-life situations without drawing a line graph.

Application Of Matrices In Real

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Matrices are used much more in daily life than people would have thought. In fact it is in front of us every day when going to work, at the university and even at home.

Graphic software such as Adobe Photoshop on your personal computer uses matrices to process linear transformations to render images. A square matrix can represent a linear transformation of a geometric object.

For example, in the Cartesian X-Y plane, the matrix reflects an object in the vertical Y axis. In a video game, this would render the upside-down mirror image of an assassin reflected in a pond of blood. If the video game has curved reflecting surfaces, such as a shiny metal shield, the matrix would be more complicated, to stretch or shrink the reflection.

In physics related applications, matrices are used in the study of electrical circuits, quantum mechanics and optics. Engineers use matrices to model physical systems and perform accurate calculations needed for complex mechanics to work. Electronics networks, airplane and spacecraft, and in chemical engineering all require perfectly calibrated computations which are obtained from matrix transformations. In hospitals, medical imaging, CAT scans and MRIs, use matrices to operate.

In robotics and automation, matrices are the basic components for the robot movements. The inputs for controlling robots are obtained based on the calculations from matrices and these are very accurate movements.

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Algebra: Types Important Topics Applications

Algebra is a branch of math dealing with several symbols. Algebra represents or helps in representing problems or situations as mathematical expressions. It comprises variables such as \. Moreover, it also involves mathematical expressions like subtraction, addition, multiplication, and division in order to generate a significant mathematical expression. Moreover, Algebra has its application in all the branches of math like trigonometry, calculus, coordinate geometry, etc. In this blog let us understand the importance of algebra.

As mentioned above, Algebra is a branch of math that deals with variables, symbols, variables, numbers and the rules for manipulating it. It helps solve mathematical equations and assists in deriving unknown quantities such as the bank interest, proportions, percentages. Thus, before we dive deep into understanding Algebra, its applications, branches, etc., let us first understand the basic terms associated with Algebra.

Read The Problem Again

Application Of Linear Algebra In Daily Life

You must read the problem carefully to understand what is given, what kind of application of linear system it is, and what is to be found. If required read it as many times as it takes.It is imperative for you to completely understand and identify all the given information and what you are being asked to find. Be mindful as at times one word can completely change how the application of a linear system is worked.

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Study Of Complex Systems

Most physical phenomena are modeled by partial differential equations. To solve them, one usually decomposes the space in which the solutions are searched into small, mutually interacting cells. For linear systems this interaction involves linear functions. For nonlinear systems, this interaction is often approximated by linear functions. In both cases, very large matrices are generally involved. Weather forecasting is a typical example, where the whole Earth atmosphere is divided in cells of, say, 100 km of width and 100 m of height.

What Are The Top Applications Of Linear Algebra

A spy detective game is one of my favorite games in my childhood. And I think you are not an exception who never play this game. In my childhood age, I always imagined how detectives decode secret messages? And I was always curious to know about it.

When I grow up, I am able to find out the method to decode the message. What is that? Well, it is one of the applications of linear algebra called Cryptography. Below, I have explained the exciting applications of linear algebra in detail. So, lets move to the details of one more concept of mathematics.

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Doing Interiors And Landscape Designing

Not only interiors planning or landscape designing, in fact, but the whole of Architecture stream employs Algebra. When the designers are trying to find the correct elevation or try to arrive upon the collection of things required to do a space, they make use of data like measurements of the space and that of the items to fit in.

This is the Algebra use in real life that helps to understand how things are going to amplify the looks of the space and will contribute to the overall appearance of the space.

Similarly, in an office environment, the decisions like moving to larger spaces to accommodate people or designing cabins are some of the premises where Algebraic calculations come into play.

Tips And Tricks To Master Algebra

Differential Equation – Introduction (2 of 16) Real Situations Represented in Differential Equations
  • Formulating a Theorem and Formula Sheets
  • Math and, inparticular, Algebra involves loads of formulas which can sometimes be confusingwhen you try to memorize them. Write down all the formulas for algebra in asheet and make it a point to review it every day so that it becomes easier tounderstand and memorize the formulas without confusion. Just make sure whileyou study these formulas and theorems, you also practice their applications.This will make the subject easier.

    2. Grasp Concepts

    While math is majorlyall about numbers, there are comprehensive concepts to help explain differentmath problems. Sometimes, students make the question harder than it is. Sostudents should make sure to read the question properly and to ensure theygrasp the problem before starting to work on the questions.

    3. Make your Basics Strong

    One can succeed in a particular field if the basic or the foundation is strong. The same thing is applicable to Algebra. Until and unless your basics of algebra are not in place, you wont be able to master the subject. Thus, make sure you clear all your doubts and have sound knowledge about the basic concepts in algebra. If required you can also take extra help to help you in understanding the basics.

    4. Practice Consistently

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    Applications Of Linear Equations

    Applications of linear equations are used by people on a daily basis even without using a line graph because the situations faced by them might have an unknown quantity that can be represented as a linear equation such as calculating mileage rates, income over time, etc. The important aspect here is the four main arithmetic operations – addition, subtraction, multiplication, and division. Let us learn more about the applications of linear equations in this article and solve some real-life examples.

    FAQs on Application of Linear Equations

    Mathematical Translation And Strategy

    Linear functions help us simplify the process of solving real-life problems. It is possible to achieve this thanks to the use of letters to represent variables and unknown values, transformation of word problems to equations, and systematic techniques to solve these equations.

    To solve problems using linear equations, we begin by translating word problems into mathematical formulations that describe the relationship between the given information and the unknowns. The key to this translation is to read the problem carefully and identify certain keywords and phrases. The following are examples of translated key phrases:

    Key phrases
    The sum of a number and 5. $latex x+5$
    Six more than a number. $latex x+6$
    Four less than a number. $latex x-4$
    Seven subtracted from a number. $latex x-7$
    The product of four and a number. $latex 4x$
    A third of a number. $latex x/3$
    The quotient of a number and 4. $latex x/4$

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    How Are Linear Equations Used In Everyday Life

    Linear equations use one or more variables where one variable is dependent on the other. Almost any situation where there is an unknown quantity can be represented by a linear equation, like figuring out income over time, calculating mileage rates, or predicting profit. Many people use linear equations every day, even if they do the calculations in their head without drawing a line graph.

    What Is The Application Of Linear Equations

    Application Of Linear Algebra In Daily Life

    The main objective for the applications of linear equations or linear systems is to solve various problems using two variables where one is known and the other is unknown, also dependent on the first. Some of these applications of linear equations are:

    • Geometry problems by using two variables.
    • Money problems by using two variables
    • A mixture of problems by using two variables.
    • Distance-Rate-Time problems by using two variables.
    • Application of linear equation in business and economics

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    Use Of Matrices In Wireless Communication

    Matrices are used to model the wireless signals and to optimise them. For detection, extractions and processing of the information embedded in signal matrices are used. Matrices play a key role in signal estimation and detection problems. They are used in sensor array signal processing and the design of adaptive filters. Matrices help in processing and representing digital images.

    We know that wireless communication is an important part of the telecommunication industry. Sensor array signal processing focuses on signal enumeration and source location applications and presents huge importance in many domains such as radar signals and underwater surveillance. The main problem in sensor array signal processing is to detect and locate the radiating sources given the temporal and spatial information collected from the sensors.

    Lets Understand It With An Example

    Assign the specific number to each alphabetical letter to encode the short secret messages.

    Then, the sequence of the number of each text should be organized in the square matrix form .

    Assume a nonsingular square matrix as B. To encode the message, multiply matrix A with matrix B . Assume the matrix B as:

    B =

    Here is the text BILA KOCKA changed into matrix A:

    and to encode the text, apply:

    Z = BA =

    Now, multiply the matrix Z to B inverse to decode the message:

    As matrix multiplication is not commutative, it must maintain the matrices with the exact product value. If you multiply the Z and B inverse matrix in the opposite order, you will obtain:

    Now, the secret message was CERNY PSIK .

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    Catch The Ball Game Played By 4

    The concept of choosing the correct trajectory so that the ball reaches the hands of the receiver comes from a kids knowledge of Algebra. By making use of variables like force, angle, and speed, the thrower tries to find the correctness of the throw of the ball. They may not have realized it, but there is no denying the fact that algebra knowledge works behind the successful landing of a ball into the hands of a receiver.

    Thus, a player can find the probability of scoring a point by doing these calculations in mind. If you are missing the target too often, the best option is to revisit the Algebra concepts and learn the needful.

    Applications Of Linear Functions In Everyday Life

    Solve Real-Life Problems Involving Linear Equations _ Algebra

    The applications of linear functions in everyday life are vast. Some common applications involve solving:

    • Age problems
    • Speed, time and distance problems
    • Geometry problems
    • Pressure and force problems
    • Salary problems

    These everyday problems are converted to mathematical forms to form linear equations, which are solved using various methods. These equations should clearly explain the relationship between the data and the variables.

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    Applications Of Linear Equations Solved Example


    Rishi is twice as old as Vani. 10 years ago his age was thrice of Vani. Find their present ages.


    In this word problem, the ages of Rishi and Vani are unknown quantities. Therefore as discussed above, let us first choose variables for the unknowns.

    Let us assume that Vanis present age is x years. Since Rishis present age is 2 times that of Vani, therefore his present age can be assumed to be 2x.

    10 years ago, Vanis age would have been x 10 , and Rishis age would have been 2x 10. According to the problem statement, 10 years ago, Rishis age was thrice of Vani, i.e. 2x 10 = 3.

    We have our linear equation in the variable x which clearly defines the problem statement. Now we can solve this linear equation easily and get the result.

    This implies that the current age of Vani is 20 years, and Rishis age is 2x, i.e. 40 years. Let us retrace our solution. If the present age of Vani is 20 years then 10 years ago her age would have been 10 years, and Rishis age would have been 30 years which satisfies our problem statement. Thus, applications of linear equations enable us to tackle such real-world problems.

    Preparing The Food Or Doubling Or Halving The Recipe

    The kitchen is one of the places where Algebra is used in an interesting manner. Especially, when you are making items like cake, vegetable soups, etc, where the correct combination of the ingredients is very crucial, Algebra comes to your rescue and helps you find the correct quantity of ingredients to make the food sufficient for different sizes of servings.

    All quantities of the ingredients and the number of servings make the variables. The cook uses Algebraic intelligence to ensure that not only the food is available in sufficient quantity, but also it is tasting great. Such is the extent of Algebra use in cooking!

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    Application Of Matrices In Mathematics

    The application of matrices in mathematics has an extended history of application in solving linear equations. Matrices are incredibly useful things that happen in many various applied areas. The application of matrices in mathematics applies to many branches of science, also as different mathematical disciplines. Engineering Mathematics is applied in our daily life.

    Use of Matrices for Collinear Point

    Matrices can be used to check whether any three given points are collinear or not. Three points suppose A, B, C are collinear if they do not form a triangle, that is the area of the triangle should be equal to zero.

    Common Examples & Applications Of Algebra In Real Life

    Class 8 Math

    Do you know who is the father of Algebra? Well, it is Muhammad ibn Musa al-Khwarizmi, a mathematician. And do you know why he is called so? Because for the first time, he introduced a system of making calculations where the numbers were replaced by variables. He employed this system of calculating for the justified appropriation of property among heirs, to improve maps by enriching them with longitudinal and latitudinal data, and also for making contributions to trigonometry, geometry, geography, etc. So, if you are thinking about why to study Algebra, the answer will be to become proficient in matters related to everyday life.

    Here are some of the most common uses of Algebra in real life that can surely help you understand how it helps you do basic activities like throwing a ball into a basketball net or cooking with the correct amount of ingredients.

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    Important Topics In Algebra

    Algebra is dividedinto various topics that help you solve equations and excel in other fields ofmathematics. Here we have listed some of the significant topics of algebra likeequations, sequence and series, exponents, logarithms, and sets. However, if youintend to make a career in Algebra, the understanding that you will need in thesubject is a little more complicated. But now is the time to make sure you getthe basics right.

    Endomorphisms And Square Matrices

    A linear endomorphism is a linear map that maps a vector space V to itself. If V has a basis of n elements, such an endomorphism is represented by a square matrix of size n.

    With respect to general linear maps, linear endomorphisms and square matrices have some specific properties that make their study an important part of linear algebra, which is used in many parts of mathematics, including geometric transformations, coordinate changes, quadratic forms, and many other part of mathematics.

    ) , }^a_\cdots a_,}

    where Sn is the group of all permutations of n elements, is a permutation, and the parity of the permutation. A matrix is invertible if and only if the determinant is invertible .

    Cramer’s rule is a closed-form expression, in terms of determinants, of the solution of a system of n linear equations in n unknowns. Cramer’s rule is useful for reasoning about the solution, but, except for n = 2 or 3, it is rarely used for computing a solution, since Gaussian elimination is a faster algorithm.

    The determinant of an endomorphism is the determinant of the matrix representing the endomorphism in terms of some ordered basis. This definition makes sense, since this determinant is independent of the choice of the basis.

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