# The Importance of the Application of Linear Algebra in Daily Life

According to Brownlee, linear algebra is the mathematics of data which matrices and vectors are the languages used in performing the data. In learning lines and planes, vector spaces and mappings, all of those required linear algebra for linear transformations. Linear algebra uses arithmetic on columns of numbers called vectors and arrays of numbers called matrices to perform new columns and arrays of numbers.

In this 21st century era world, we cannot deny that there are a lot of applications that uses the mathematical concepts of linear algebra in daily life. One of the applications is regarding to the Electrical Networking work field. In real life, electrical engineers use electrical networks to build up circuits or make stereotype for circuits. The electrical engineers could implement the concepts of linear algebra in identify the linearity relationship between the voltage and the current yet solving daily life problems involving electrical circuits. There are mainly three basic laws: Ohm’s Law, Kirchhoff’s Voltage Law (Conservation of Energy) and Kirchhoff’s Current Law (Conservation of Charge) in controlling the flow of current in an electrical circuit. Hence, with the basic laws, together with given or predicted with a specific detail of currents, resistance and potential difference in a circuit, electrical engineers would be able to generate equations with multiple unknowns, forming linear system from the circuits building. With linear system, electrical engineers can be solved by incepting the methods of Linear Algebra in finding the unknown values of quantities. Furthermore, linear algebra is said to be more useful when the network system has many unknowns.

Besides, according to Berger, a Markov Chains is an application of linear algebra. A Markov Chains are designed to model systems that change form a state to another state. He also stated that the current state should depend only on the previous state. In other words, we can say that Markov Chains give an ideology that a future distribution can be formed depends on the most recent previous distribution. Markov chains can be used to model situations in many fields, including biology, physics, chemistry and economic. The most common applications are in predicting the populations growth, weather forecasting purpose and many more. The forecasters will identify the changes that depend on the immediate history of a system before making any inferences about the future system. Hence, in applying linear algebra in Markov Chains, forecasters can implement the concept of linear algebra to predict future conditions or situations. In addition, by applying linear algebra and matrix method in Markov Chains, human will be presented with a chronological view while monitoring the progress of a system throughout the whole discrete time intervals.

According to Isaac, Douglas & Vincent, linear algebra can be used in civil engineering. With applying linear algebra, a civil engineer can develop an optimal road network with efficient movement of traffic. In other words, creating an effective traffic flow to improve overall transportation system’s sustainability with minimal traffic congestion problems in real life. Traffic congestion is a global phenomenon resulting from high population density and the rapid growth of motor vehicles as we cannot deny that human keen to own vehicles for self-transportation. Consequently, disruptions to transportation networks such as traffic congestion often occur and still increasing throughout time. Traffic congestion will bring negative impacts, causing delays, inconvenience, and economic losses to drivers, as well as air pollution. As passengers used up excess travel time which may cause late arrival for employment and educations yet leading to failure in business progress and personal losses. In addition, traffic congestion will cause interference toward emergency vehicles which the passengers wish to arrive in a destination urgently. Therefore, it is important for civil engineering to carry out linear algebra in solving problems regarding traffic flow in real world situations, developing a sustainable and resilient traffic management system for the citizens.

In other words, linear algebra can be identified as the study of linear combinations. With the knowledge of elementary linear algebra, one can build a strong computational framework and yet contributing in solving real-life situations. In mastering elementary linear algebra concept, we can implement the knowledge yet solving problems that enquire function of several variables more realistic expression in the real world.

07 July 2022

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