Definitions for linear equation
lin·ear equa·tion

Princeton's WordNetRate this definition:0.0 / 0 votes

1. linear equationnoun

   a polynomial equation of the first degree

WiktionaryRate this definition:0.0 / 0 votes

1. linear equationnoun

   A polynomial equation of the first degree (such as x = 2y - 7)

WikipediaRate this definition:0.0 / 0 votes

1. Linear equation

   In mathematics, a linear equation is an equation that may be put in the form a 1 x 1 + … + a n x n + b = 0 , {\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0,} where x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} are the variables (or unknowns), and b , a 1 , … , a n {\displaystyle b,a_{1},\ldots ,a_{n}} are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients a 1 , … , a n {\displaystyle a_{1},\ldots ,a_{n}} are required to not all be zero. Alternatively, a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken. The solutions of such an equation are the values that, when substituted for the unknowns, make the equality true. In the case of just one variable, there is exactly one solution (provided that a 1 ≠ 0 {\displaystyle a_{1}\neq 0} ). Often, the term linear equation refers implicitly to this particular case, in which the variable is sensibly called the unknown. In the case of two variables, each solution may be interpreted as the Cartesian coordinates of a point of the Euclidean plane. The solutions of a linear equation form a line in the Euclidean plane, and, conversely, every line can be viewed as the set of all solutions of a linear equation in two variables. This is the origin of the term linear for describing this type of equations. More generally, the solutions of a linear equation in n variables form a hyperplane (a subspace of dimension n − 1) in the Euclidean space of dimension n. Linear equations occur frequently in all mathematics and their applications in physics and engineering, partly because non-linear systems are often well approximated by linear equations. This article considers the case of a single equation with coefficients from the field of real numbers, for which one studies the real solutions. All of its content applies to complex solutions and, more generally, for linear equations with coefficients and solutions in any field. For the case of several simultaneous linear equations, see system of linear equations.

ChatGPTRate this definition:0.0 / 0 votes

1. linear equation

   A linear equation is a mathematical expression that has an equal sign and linear expressions. A linear equation may have one, two, or more variables. It is called a linear equation because its graphical representation is a straight line in a coordinate system. The standard and most common form of a linear equation is "y = mx + b", where m represents the slope of the line and b represents the y-intercept.

WikidataRate this definition:5.0 / 1 vote

1. Linear equation

   A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. Linear equations can have one or more variables. Linear equations occur with great regularity in applied mathematics. While they arise quite naturally when modeling many phenomena, they are particularly useful since many non-linear equations may be reduced to linear equations by assuming that quantities of interest vary to only a small extent from some "background" state. Linear equations do not include exponents.

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1. • Equation

How to pronounce linear equation?

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How to say linear equation in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of linear equation in Chaldean Numerology is: 2

2. Pythagorean Numerology

   The numerical value of linear equation in Pythagorean Numerology is: 8

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=linear equation
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Linear_Equation
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Linear_Equation
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=linear equation