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Because a solution to a linear system must satisfy all of the equations, the solution set is the intersection of these lines, and is hence either a line, a single point, or the empty set. For three variables, each linear equation determines a plane in three-dimensional space , and the solution set is the intersection of these planes.
In mathematics, the solution set of a system of equations or inequality is the set of all its solutions, that is the values that satisfy all equations and inequalities. [1] Also, the solution set or the truth set of a statement or a predicate is the set of all values that satisfy it. If there is no solution, the solution set is the empty set. [2]
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as:
This, the authors hope, might provide clearer answers. They recruited 1,220 participants in a hospital: 876 females and 344 males. All were aged 60 or older and hospitalized at the time of the study.
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A subset V of A n is called an affine algebraic set if V = Z(S) for some S. [1]: 2 A nonempty affine algebraic set V is called irreducible if it cannot be written as the union of two proper algebraic subsets. [1]: 3 An irreducible affine algebraic set is also called an affine variety.
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