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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 !!
What else can I help you with?
What are real life situations which are applications of linear equations?
Cell phone companies
Does the range of linear equations have all real numbers?
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.
What is a real life example of linear equations?
A real-life example of linear equations can be found in budgeting. For instance, if you earn a fixed salary of $3,000 per month and have fixed expenses like rent ($1,200) and utilities ($300), you can represent your savings as a linear equation: S = 3000 - (1200 + 300) - x, where S is your savings and x represents any additional expenses. This equation allows you to see how changes in your spending impact your savings over time.
Solve linear equations with complex coefficients on both sides?
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.
Do you use two step equations in real life?
no
How can you use solving equations in real life?
School is part of real life... if you are using equations in school that is real.
What are real life situations which are applications of linear equations?
Cell phone companies
Does the range of linear equations have all real numbers?
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.
What is a real life example of linear equations?
A real-life example of linear equations can be found in budgeting. For instance, if you earn a fixed salary of $3,000 per month and have fixed expenses like rent ($1,200) and utilities ($300), you can represent your savings as a linear equation: S = 3000 - (1200 + 300) - x, where S is your savings and x represents any additional expenses. This equation allows you to see how changes in your spending impact your savings over time.
Solve linear equations with complex coefficients on both sides?
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.
How do you solve imaginary equations?
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.
How do you use equations in real life?
architecture jobs
Do you use two step equations in real life?
no
Use of linear function in real life?
Your age is a linear function (of time).
How can you use matrices to solve real world problems?
Matrices are tools to solve linear equations. Engineers use matrices in solving electrical problems in circuits using Thevenin's and Norton's theories.
When you have two linear equations how do you know when they are all real numbers?
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.
What are the Sample problems in differential equations?
Sample problems in differential equations often include finding the solution to first-order equations, such as separable equations or linear equations. For example, solving the equation ( \frac{dy}{dx} = y - x ) involves using integrating factors or separation of variables. Other common problems include second-order linear differential equations, like ( y'' + 3y' + 2y = 0 ), where the characteristic equation helps find the general solution. Applications may involve modeling real-world phenomena, such as population growth or the motion of a pendulum.
