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 MRI’s, use matrices to operate.
Whereas in programming which is taught at the university, matrices and inverse matrices are used for coding and encrypting messages. A message is made as a sequence of numbers in a binary format for communication and it follows code theory for solving.
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.
Many IT companies also use matrices as data structures to track user information, perform search queries, and manage databases. In the world of information security, many systems are designed to work with matrices. Matrices are used in the compression of electronic information, for example in the storage of biometric data in the new Identity Card in Mauritius.
In geology, matrices are used for making seismic surveys. They are used for plotting graphs, statistics and also to do scientific studies and research in almost different fields. Matrices are also used in representing the real world data’s like the population of people, infant mortality rate, etc. They are best representation methods for plotting surveys. In economics very large matrices are used for optimization of problems, for example in making the best use of assets, whether labour or capital, in the manufacturing of a product and managing very large supply chains.
Application of Statistics in real-life problems.
Statistics can be defined as a type of mathematical analysis which involves the method of collecting and analyzing data and then summing up the data into a numerical form for a given set of factual data or real world observations.
In our daily life, we collect information which helps us in resolving questions regarding the world in which we live, that is statistics.
One main example is weather forecast. These charts and information that you see on the television are obtained using statistics that compare last weather conditions with current weather to predict future weather.
Whenever there’s an election as the one coming in a few days in Mauritius, the press consult statistical surveys with the population when they try to predict the winner. Candidates use statistics to know for example that 20,000 of these voters will be between the age of 18 and 22, that is this will be their first election and thus try to focus their campaign more on benefits for these young adults. Statistics play a part in which your elected government will be consisted of.
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In industries and businesses it is crucial to be fast and accurate in decision making. They use statistics to know what customers want and therefore know what to produce and sell and in what quantities. Statistics helps to plan production according to the taste of the customers, the quality of the products or availability of materials. Good decisions can be made about the location of business, marketing of the products, financial resources etc…
Statistics are also used in agriculture to know what amount of crops is grown this year in comparison to previous years or what has been the demand for a certain crop during the past 5 years or quality and size of vegetables grown due to use of different fertilizers.
Last Friday was the results day for the CPE exams in Mauritius and statistics were used to compare the different pass rates for girls compared to boys and how the whole pass rate have evolved during the past years. These statistics helps the government to determine whether the education system in the country needs to be modified or completely re-implemented.
In medical studies scientists must show a statistically valid rate of efficacy before any drug can start to be prescribed in hospitals and pharmacies. Statistics are behind every medical study you hear about. For example an ongoing case, the Ebola virus. Statistics are used to determine the number of infected persons in different countries and these data helps to warn neighbouring countries about the risks they are exposed to.
Application of Regression in real-life problems.
Correlation and regression are largely used methods to look into the relationships between quantitative variables. A correlation looks at the validity of the relationship between variables and regression helps to determine the nature of the relationship, or how it behaves. This allows predictions to be made. These methods are very useful, but easily misused.
Regressions can be used in business to evaluate trends and make estimates. For e.g. if a company’s sales have increased rapidly every month for the past years, using a linear regression on the sales data with monthly sales on the y-axis and time on the x-axis would produce a line that illustrates the ascending trend in sales. After obtaining the trend line, the company could use the slope of the line to anticipate sales in future months.
A company can use linear regression to determine the best sale price for a certain product bought by customers. This can be done by plotting a graph of price against quantity. The resulting line would denote how customers reduce their consumption of the product as the price increases. This could help in decision making of the prices of future products.
Linear regression can be used in assessing risk. For e.g. a health insurance company shall plot number of claims per customer against age and by reading the graph deduce that older customers tend to make more health insurance claims. The results of such an analysis might lead to important business decisions made to account for risks.
Application of Correlation in real-life problems.
For e.g. a researcher suggested that taller people have higher self-esteem. After analyzing his data and coming up with an r-value of .08, he abandons his hypothesis because the two variables do not appear to be strongly related at all.
Another area where correlation is used is in the study of intelligence where research has been carried out to test the strength of the relationship between the I.Q. levels of identical and non-identical twins.
In medical studies, correlation is used widely and one e.g. is the study to test if glucose level is related to the age of a person.
Correlation is mostly used in research studies. In schools for e.g. a use of correlation would be the study of how a student who has many absences has a decrease in grades or the more years of education you complete, the higher your earning potential will be.
In the sports area correlation is used broadly by coaches to develop workout routines. Some common correlations are: the more time a person spends running on a treadmill, the more calories he will burn or the more you exercise your core muscles, the more stable your body gets.
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