Linear system of equations and its solution(s)

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SUMMARY

A system of linear algebraic equations can have one solution, zero solutions, or infinite solutions, but it cannot have multiple finite solutions. When a system has infinite solutions, the equations are dependent and represent the same line graphically. The intersection of lines in a graphical representation indicates the solutions, where multiple lines can intersect at a single point or not at all, but never at a finite number of distinct points.

PREREQUISITES
  • Understanding of linear algebra concepts
  • Familiarity with systems of equations
  • Knowledge of graphical representation of equations
  • Basic skills in algebraic manipulation
NEXT STEPS
  • Study the properties of linear dependence and independence in equations
  • Learn about graphical solutions of linear systems using tools like GeoGebra
  • Explore the concept of solution spaces in linear algebra
  • Investigate the implications of infinite solutions in real-world applications
USEFUL FOR

Students of mathematics, educators teaching linear algebra, and professionals working with mathematical modeling and systems of equations.

fisico30
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Hello Forum,

a system of linear algebraic equations can have 1 solution, zero solutions, or infinite solutions.

Can it ever have multiple, finite solutions? Why not?

when the system has infinite solutions, are the equations representing all the same identical equation, i.e. they are all dependent? Graphically, the solution space is a straight line...

thanks,
fisico30
 
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fisico30 said:
Hello Forum,

a system of linear algebraic equations can have 1 solution, zero solutions, or infinite solutions.

Can it ever have multiple, finite solutions? Why not?

Graphically, a solution to a system of linear equations would be a point where all of the lines intersect. Can two or more lines intersect at a finite number of points?
 

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