# 9 Common Applications Of Determinants In Real-life

Mathematics is a fundamental part of life required in various other study areas, such as science, finance, statistics, etc. The study of mathematics is not limited to theoretical concepts; rather, you will find that most mathematical concepts like probability, and fibonacci sequence are applied in real life. The credit for the advancement of technology goes equally to mathematical concepts and the genius minds who developed them.

However, understanding these mathematical concepts can be challenging for students as merely understanding the theoretical use of mathematical concepts can be monotonous. These issues can be overcome by adding real-life applications of mathematical concepts in the teaching lessons.

Teachers can use or demonstrate real-life applications of mathematical concepts to make the concept more clear and engaging. In this article, we have curated a list of real-life applications of determinants- a highly crucial topic that has its uses in multiple professions. Before moving to the real-life application, let’s understand what determinants are.

## What are determinants?

Determinants are a highly essential mathematical concept used for simplifying complex linear algebraic problems, solving calculus problems, and finding inverse of a matrix. It also plays a key role in daily life, making its understanding crucial. Determinants are any scalar value that can be obtained from the products of the elements of a square matrix.

Let’s understand what determinants are with the help of an example

Suppose you are the owner of a small flower shop. Your trademark products like bouquet, tiaras, etc., revolve around two major types of flowers: lavender and orchids. You want to keep a track on how these three flowers in total are contributing to your sales.

Let’s say, lavender bought you an income of \$100 and orchids contributed \$150 on week 1. Similarly, revenue bought by lavender is \$80, and orchids is \$200 on week 2. To find the total contribution of each flower for the last 15 days in your overall sales you can use the concept of determinants and set up a matrix to find the overall income generated by these three flowers.

Sales matrix:
|100  150|
|80    200|

We can solve it using a 2×2 matrix formula,
(ad)- (bc)
(100×200) – (150 × 80) = 20000- 12000
= 8000

The total revenue generated by the lavender and orchids in the past 15 days is 8000.

## Real-life application of determinants

The use of determinants is multifold, involved in multiple domains, and is a common example of inductive and deductive reasoning in daily life. Plotting graphs, conducting scientific studies, applying statistical applications, etc., determinants are used in many areas as discussed in detail below –

### 1. Designing 3D space for gaming, virtual interior designing models, etc.

Determinants play an important role in designing a 3D space for various purposes such as games, virtual interior design models, etc. For instance, developing 3D games or converting 2D games into 3D games requires matrix spaces, that is a certain number of rows and columns for identifying an estimated space, and the value of determinants for accurately creating the gaming area.

Additionally, determinants help develop 3D space where the game’s characters will be visually present. Similarly, placing objects in virtual 3D space requires the knowledge of determinants.

### 2. Virtual construction designs

Determinants are a handy tool for civic engineers and an important part of making blueprints for constructing buildings. Blueprints could either be physical or virtual and both are designed on the basis of matrix and determinants.

Different parts of the houses are represented on a blueprint with an accurate measurement that requires matrices and determinants. It helps better represent the measurements and enhances understanding of the tasks for constructing a building.

### 3. Studying the characteristics of the circuits

Analyzing circuits is another important area where determinants are widely used. Studying determinants is an unavoidable part of engineering and electrical engineers analyze the characteristics and develop the structure of the circuits through the knowledge and practical use of determinants. Electrical engineers also use the concept of determinants to solve complex circuits and simplify them.

### 4. Digital Arts and Graphics

Determinants are also applied to creative fields such as graphic designing, digital art, and poster making. Incorporating various design elements and organizing them requires using pixels distributed in various rows and columns. These pixels help represent and structure the various elements required to make the art appealing and organized. Computer graphics also require the use of determinants.

### 5. To study waves, currents, and frequencies

Determinants play an important role in various geographical studies, such as the study of seismic waves (responsible for earthquakes) or currents. Assessing how fast and large the waves or currents were and the duration of their impact can be successfully done through matrices and determinants. Similarly, sound waves or vibrations from different sources can be studied or simplified using the concepts of determinants and matrices.

### 6. Practical concepts of physics like quantum mechanics

The field of mathematics and physics goes hand in hand. If determinants are important in mathematics, it will also be important for the study of physics. Various practical concepts of physics, such as quantum mechanics, resistors, electrical circuits, different energy forms, voltage and its various laws, eigenvalues, eigenvectors, optics, batteries, etc., all work on the principles of determinants.

Determinants simplify and enhance the practicality of the mentioned fields, therefore, advanced knowledge of determinants is necessary while dealing with the concepts of physics.

### 7. Analyzing Business trends and economic trends

Business trends and details are represented using graphical structures or tables requiring determinants. Graphs are of various types, such as bar graphs, histograms, pie charts, etc., and are used for different purposes, such as analyzing stock market trends, economic growth and decline, shares, etc. Determinants simplify the formation, use, and structuring of graphs, making them convenient to use.

### 8. Cryptography: Making communication safe

Cryptography is securing communication or information in the digital landscape using mathematical concepts. Messages, bank cards, important passcodes, e-commerce banking details, etc., are all protected through cryptography. Determinants play a crucial role in designing cryptographic patterns and making information and communication secure.

### 9. Analyzing demographics

Analyzing demographics is another important real-life application of determinants. Analyzing the increment or decrement in the population and studying the changing demographic trends are based on the knowledge of determinants. Formulating charts and reports on the demographics also requires the use of determinants.

Determinants is a widely used mathematical concept, and the list of its real-life applications is long. We hope, by now, you have some idea of how determinants are applied in our day-to-day life.

## Concluding thoughts

Determinants are used in various scientific and mathematical domains, making them important concepts. Like other mathematical concepts, determinants involve deductive reasoning and different strategies of discovery approach in mathematics for its understanding. For effectively applying the concepts of determinants in real-life situations, logical thinking is important.

At a very basic level, determinants can simplify complex mathematical concepts, whereas, on an advanced level, determinants are required for complex real-life situations, such as studying earthquakes, making economic reports, etc. Educators can enhance the learning of determinants by including these real-life applications or activities.