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A system of word equations is called independent if it is not equivalent to any of its proper subsystems. [16] Put another way, an independent system S {\displaystyle S} of word equations is one such that every E ∈ S {\displaystyle E\in S} can be solved "independently", i.e., without solving any of the other E ′ ∈ S {\displaystyle E'\in S} .
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a: System of linear equations, System of nonlinear equations,
Two equations or two systems of equations are equivalent, if they have the same set of solutions. The following operations transform an equation or a system of equations into an equivalent one – provided that the operations are meaningful for the expressions they are applied to: Adding or subtracting the same quantity to both sides of an ...
A computer desktop, with various folders and files visible The computer interface is a conceptual metaphor of a writing desk.. In computing, the desktop metaphor is an interface metaphor which is a set of unifying concepts used by graphical user interfaces to help users interact more easily with the computer. [1]
In these equations, g 0, M and R * are each single-valued constants, while P, L, T, and h are multivalued constants in accordance with the table below. The values used for M , g 0 , and R * are in accordance with the U.S. Standard Atmosphere , 1976, and the value for R * in particular does not agree with standard values for this constant. [ 2 ]
The templates {} and {{EquationRef}} can be used to number equations. The template {{EquationNote}} can be used to refer to a numbered equation from surrounding text. For example, the following syntax: {{NumBlk |: |< math > x ^ 2 + y ^ 2 + z ^ 2 = 1 </ math >|{{EquationRef | 1}}}} produces the following result (note the equation number in the ...
Download and install System Mechanic Everyday PC usage can take its toll on computer and PC systems, making them annoyingly slow. System Mechanic, from iolo, is a software suite that secures, optimizes, repairs and fine tunes your computer after five restarts so the system can run faster and at its best.
The rank of a system of equations (that is, the rank of the augmented matrix) can never be higher than [the number of variables] + 1, which means that a system with any number of equations can always be reduced to a system that has a number of independent equations that is at most equal to [the number of variables] + 1.