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When you have two linear equations how do you know when they are all real numbers?
Wiki User
∙ 12y ago
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.
Wiki User
∙ 9y ago
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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 are real life situations which are applications of linear equations?
Cell phone companies
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.
What is the domain of all quadratic equations?
The set of all real numbers. Or all complex numbers, depending what you decide to use as your basic set.
What is the use of gaussian elimination in real world situations?
The gaussian elimination is used to solve many linear equations with many unknown varaibles at once. [See related link below to find out how to do it]. This is used alot by engineers you know ceratin variables in there structures and want to find out what the stress and strain is in certain areas. They make up there linear equations and then they can use the gaussian elimination method to find the unknown variables.
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 are real life situations which are applications of linear equations?
Cell phone companies
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.
What is the domain of all quadratic equations?
The set of all real numbers. Or all complex numbers, depending what you decide to use as your basic set.
What is the use of gaussian elimination in real world situations?
The gaussian elimination is used to solve many linear equations with many unknown varaibles at once. [See related link below to find out how to do it]. This is used alot by engineers you know ceratin variables in there structures and want to find out what the stress and strain is in certain areas. They make up there linear equations and then they can use the gaussian elimination method to find the unknown variables.
What math comes after calculus?
Differential equations, Linear Algebra, Abstract Algebra, Real and Complex Analysis, Advanced Calculus, and lots of other fun stuff.
What is linear algebra used for?
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.
What are the differences between real numbers and imaginary numbers?
The set of real numbers is not closed under powers. That is to say, there are some equations of the form y = xa which do not have a solution within the set. Typical example: x is negative, a = 0.5
Can you solve system of equations by graphing?
Yes you can, if the solution or solutions is/are real. -- Draw the graphs of both equations on the same coordinate space on the same piece of graph paper. -- Any point that's on both graphs, i.e. where they cross, is a solution of the system of equations. -- If both equations are linear, then there can't be more than one such point.
Family tree of real numbers?
Start with the set of Natural numbers = N.Combine these with negative natural numbers and you get the set of Integers = Z.Combine these with ratios of two integers, the second of which is positive, and you get the set of Rational numbers = Q.Start afresh with numbers which are not rational, nor the roots of finite polynomial equations. This is the set of transcendental numbers.Combine these with the non-rational roots of finite polynomial equations and you have the set of irrational numbers.Combine the rational and irrational numbers and you have the set of Real numbers, R.
What has only one solution?
There are many possible answers to this question. Some of these areA linear equation.A system of n independent linear simultaneous equations is n unknowns.Quadratic equations in which the two real roots are coincident.Cubic equation where either all three roots are coincident or, if the domain is real, then when two of the roots are imaginary.
