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I image you intends algebraic linear equations. A great number of problems in real life are mathematically model with algebraic linear equations like

- Design of electronic filters for any application (smart-phones, stereo systems, radio systems, ....)

- Optimization of the any problem that can be modeled with the so called simplex algorithm (commercial programs uses this set of linear equations to optimize management of a civil airplane company, of the production in a car factory, of the management of a warehouse and many other problems)

- The determination of currents and voltages in an electrical circuit composed of resistances, inductive elements, capacitors and ideal amplifiers can be done by a system of algebraic linear equations;

This is only a very limited set of examples.

However in mathematics any equation, not only algebraic, but also integral, differential and so on, is called linear if the sum of two solutions is again a solution and the product of a solution by a number is again a solution. You can easily verify that it is true also for homogeneous algebraic equations (that is linear angebraic equations without the known term). For example if we have the two unknown x and y the equation

2x+y=0

is linear. As a matter of fact, since x=1, y=-2 is a solution and x=-2, y=4 is another solution, also the sum of the two solutions, that is x=-1, y=2 is another solution.

If we adopt this extended definition, the quantum mechanical basic equations are linear, thus we can say that, up to the moment in which we do not consider cosmic bodies for whom gravity is important, the whole world is linear !!

Q: Using linear equations in real life?

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Cell phone companies

No. For example, linear algebra, for example, is about linear equations where the domain and range are matrices, not simple numbers. These matrices may themselves contain numbers that are real or complex so that not only is the range not the real numbers, but it is not based on real numbers either.

You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.

no

Your age is a linear function (of time).

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School is part of real life... if you are using equations in school that is real.

Cell phone companies

No. For example, linear algebra, for example, is about linear equations where the domain and range are matrices, not simple numbers. These matrices may themselves contain numbers that are real or complex so that not only is the range not the real numbers, but it is not based on real numbers either.

You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.

The answer depends on the nature of the equation. Just as there are different ways of solving a linear equation with a real solution and a quadratic equation with real solutions, and other kinds of equations, there are different methods for solving different kinds of imaginary equations.

Matrices are tools to solve linear equations. Engineers use matrices in solving electrical problems in circuits using Thevenin's and Norton's theories.

architecture jobs

no

Your age is a linear function (of time).

The answer depends on what are meant to be real numbers! If all the coefficients are real and the matrix of coefficients is non-singular, then the value of each variable is real.

Linear algebra is used to analyze systems of linear equations. Oftentimes, these systems of linear equations are very large, making up many, many equations and are many dimensions large. While students should never have to expect with anything larger than 5 dimensions (R5 space), in real life, you might be dealing with problems which have 20 dimensions to them (such as in economics, where there are many variables). Linear algebra answers many questions. Some of these questions are: How many free variables do I have in a system of equations? What are the solutions to a system of equations? If there are an infinite number of solutions, how many dimensions do the solutions span? What is the kernel space or null space of a system of equations (under what conditions can a non-trivial solution to the system be zero?) Linear algebra is also immensely valuable when continuing into more advanced math topics, as you reuse many of the basic principals, such as subspaces, basis, eigenvalues and not to mention a greatly increased ability to understand a system of equations.

Creating an abstract system of equations which describes (and helps reasoning about) a real life system.