Solving a System of Equations in Linear Algebra

In summary, a system of equations in linear algebra is a set of two or more equations that involve the same variables, and its solution is a set of values that satisfies all of the equations. To solve a system of equations, various methods such as substitution, elimination, or graphing can be used. A system of equations can have one or infinitely many solutions, and having no solution means that there is no set of values that satisfies all of the equations. Solving a system of equations is useful in real-life situations such as finding intersection points, optimizing solutions, or solving for unknown variables in scientific experiments. It is also crucial in engineering and physics for solving complex systems that model real-world phenomena.
  • #1
kasse
384
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In a city there are four one-way streets that cross each other like this:

http://www.badongo.com/pic/1751680

The number of cars that pass every hour is shown.

Show that x=(x1,x2,x3,x4) satisfies a system on the form

Ax=b
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I really have no clue what to to here.
 
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  • #2
There are cars coming in, and coming out of each direction. The difference (out - in) is the number of cars that take a turn into another segment. Similar to a Markov problem.
 

FAQ: Solving a System of Equations in Linear Algebra

What is a system of equations in linear algebra?

A system of equations in linear algebra is a set of two or more equations that involve the same variables. The solution to the system is a set of values for the variables that satisfies all of the equations.

How do you solve a system of equations?

To solve a system of equations, you can use various methods such as substitution, elimination, or graphing. The goal is to manipulate the equations to isolate one variable and then substitute that value into the other equations to find the values of the remaining variables.

Can a system of equations have more than one solution?

Yes, a system of equations can have one or infinitely many solutions. If the equations are consistent and have the same number of equations as variables, then there will be a unique solution. However, if there are more variables than equations, then there will be infinitely many solutions.

What does it mean if a system of equations has no solution?

If a system of equations has no solution, it means that there is no set of values for the variables that satisfies all of the equations. This can occur if the equations are inconsistent, meaning they contradict each other, or if there are more equations than variables.

How is solving a system of equations useful in real life?

Solving a system of equations is useful in various real-life scenarios such as calculating the intersection point of two lines, finding the optimal solution in business or economics, or solving for unknown variables in scientific experiments. It is also a fundamental concept in engineering and physics for solving complex systems of equations that model real-world phenomena.

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