dependent system

(noun)

A system of linear equations in which the two equations represent the same line; there are an infinite number of solutions to a dependent system.

Related Terms

  • To find the unique solution to a system of linear equations, we must find a numerical value for each variable in the system that will satisfy all equations in the system at the same time.
  • solution to a system of linear equations
  • numerical value for each variable in the system that will satisfy all equations in the system at the same time.
  • system of linear equations
  • independent system
  • inconsistent system

Examples of dependent system in the following topics:

  • Inconsistent and Dependent Systems in Two Variables

    • For linear equations in two variables, inconsistent systems have no solution, while dependent systems have infinitely many solutions.
    • An inconsistent system has no solution, and a dependent system has an infinite number of solutions.
    • We will now focus on identifying dependent and inconsistent systems of linear equations.
    • Systems that are not independent are by definition dependent.
    • We can apply the substitution or elimination methods for solving systems of equations to identify dependent systems.
  • Inconsistent and Dependent Systems in Three Variables

    • Systems of equations in three variables are either independent, dependent, or inconsistent; each case can be established algebraically and represented graphically.
    • Dependent systems have an infinite number of solutions.
    • We know from working with systems of equations in two variables that a dependent system of equations has an infinite number of solutions.
    • The same is true for dependent systems of equations in three variables.
    • Explain what it means, graphically, for systems of equations in three variables to be inconsistent or dependent, as well as how to recognize algebraically when this is the case
  • Inconsistent and Dependent Systems

    • ) and dependency (are the equations linearly independent?
    • Systems that are not independent are by definition dependent.
    • are dependent, because the third equation is the sum of the other two.
    • In general, inconsistencies occur if the left-hand sides of the equations in a system are linearly dependent, and the constant terms do not satisfy the dependence relation.
    • The equations x − 2y = −1, 3x + 5y = 8, and 4x + 3y = 7 are not linearly independent, i.e. are dependent.
  • Introduction to Systems of Equations

    • A system of equations consists of two or more equations with two or more variables, where any solution must satisfy all of the equations in the system at the same time.
    • To find the unique solution to a system of linear equations, we must find a numerical value for each variable in the system that will satisfy all of the system's equations at the same time.
    • A solution to the system above is given by
    • An inconsistent system has no solution.
    • A dependent system has infinitely many solutions.
  • Open and Closed Circulatory Systems

    • The circulatory system can either be open or closed, depending on whether the blood flows freely in a cavity or is contained in vessels.
    • In a closed circulatory system, blood is contained inside blood vessels, circulating unidirectionally (in one direction) from the heart around the systemic circulatory route, then returning to the heart again.
    • In contrast to a closed system, arthropods (including insects, crustaceans, and most mollusks) have an open circulatory system.
    • Most vertebrates and some invertebrates, such as this annelid earthworm, have a closed circulatory system.
    • Arthropods, such as this bee and most mollusks, have open circulatory systems.
  • World-Systems Theory

    • World Systems Theory posits that there is a world economic system in which some countries benefit while others are exploited.
    • India is an example of a semi-peripheral country -- it is largely dependent on foreign investors for capital, but has a growing technology industry and emerging middle class consumer market.
    • World Systems Theory, like dependency theory, suggests that wealthy countries benefit from other countries and exploit those countries' citizens.
    • In contrast to dependency theory, however, this model recognizes the minimal benefits that are enjoyed by low status countries in the world system.
    • Peripheral countries (e.g., most African countries and low income countries in South America) are dependent on core countries for capital and are less industrialized and urbanized.
  • Matrix Equations

    • Matrices can be used to compactly write and work with systems of multiple linear equations.
    • Matrices can be used to compactly write and work with systems of equations.
    • This is very helpful when we start to work with systems of equations.
    • Thus, we want to solve a system $AX=B$, for $X$.  
    • No, if the coefficient matrix is not invertible, the system could be inconsistent and have no solution, or be dependent and have infinitely many solutions.
  • Comparison of Enthalpy to Internal Energy

    • A thermodynamic system can be any physical system with a well-defined volume in space.
    • Internal energy is a state function, meaning its value is dependent only on the current state of the system.
    • Hence, -q means the system loses heat, while +q means a system gains heat.
    • Similarly, +w means work is done on the system, while -w means work is done by the system.
    • However, in open systems, the pressure of the system and the surroundings has stayed constant.
  • Inadequate or incorrect internal accounting and dependence on third parties

    • All firms, whether young or mature, need cost accounting systems which can report costs and—as far as they are specifically attributable—revenues per cost unit, cost center, and department.
    • It is important that start-ups establish systems for unit cost accounting, cost center accounting, and breakeven analysis (cf.
    • However, the older the firm becomes, dependence on third parties should be reduced.
    • The dependence on licensors should be compensated for by the firm's own research and development.
    • As shown above, dependence on third parties can arise when a firm markets its products.
  • Pressure and Free Energy

    • Gibbs free energy measures the useful work obtainable from a thermodynamic system at a constant temperature and pressure.
    • The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system.
    • When a system changes from an initial state to a final state, the Gibbs free energy (ΔG) equals the work exchanged by the system with its surroundings, minus the work of the pressure force.
    • Gibbs energy (also referred to as ∆G) is also the chemical potential that is minimized when a system reaches equilibrium at constant pressure and temperature.
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