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Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.

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Q: Is linear algebra and linear equations the same?
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What is the definition of Simultaneous Linear Equations?

A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.


What is cramer rule?

In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.


What is the relationship between linear algebra and economics?

Many problems in economics can be modelled by a system of linear equations: equalities r inequalities. Such systems are best solved using matrix algebra.


How does solving a literal equation differ from solving a linear equation?

Because linear equations are based on algebra equal to each other whereas literal equations are based on solving for one variable.


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.

Related questions

What has the author Arthur Sylvester Peters written?

Arthur Sylvester Peters has written: 'Lectures on linear algebra' -- subject(s): Differential equations, Linear, Linear Differential equations 'Linear algebra' -- subject(s): Algebra


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 definition of Simultaneous Linear Equations?

A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.


Is there an online site for algebra worksheets?

There are a variety of algebra worksheets available at www.kutasoftware.com. Some include basic algebra, polynomials and linear equations.


What are two or more linear equations using the same variables called?

A system of linear equations.


What is cramer rule?

In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.


What is a group of linear equations that use the same variables?

a system of equations


What are linear equations with the same solutions called?

They are called simultaneous equations.


How are linear inequalities and linear equations the same?

They are not. An inequality cannot, by definition, be the same as an equation.


What is the relationship between linear algebra and economics?

Many problems in economics can be modelled by a system of linear equations: equalities r inequalities. Such systems are best solved using matrix algebra.


How does solving a literal equation differ from solving a linear equation?

Because linear equations are based on algebra equal to each other whereas literal equations are based on solving for one variable.


Is linear algebra the same as geometry?

No, geometry is more depth into algebra, with formulas and shapes. That's why algebra is a prerequisite

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