Examples of dependent system in the following topics:
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- 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.
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- 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
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- ) 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.
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- 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.
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- 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.
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- 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.
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- 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.
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- 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.
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- 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.
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- 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.