Skip to main content

Definition of Linear Equation

Any straight line in the XY plane can be represented algebraically by an equation of the form

a1x1 + a2x2 + - - - - - - + anxn = b ----------------------- (1)

Where a1, a2 - - - - - - an and b are real constants. An equation of this form is called Linear Equation in the variables x1, x2 - - - - - - xn . The variables in a linear equation are sometimes called Unknown.

Comments

strangerland said…
Well someone sent me a link to your blog Rashad, since I frequently post math in my blog. One of my interests is the application of linear algebra to graph theory. My most recent posts have been about the free software package called SAGE. I'm trying to learn how to use SAGE and Python in order to explore the application of Free Boolean Algebra to a combinatorics problem in Graph Theory and Linear Algebra. It looks like it's a good package for the problems you posed in your blog. Keep blogging about math.
Well, I am here to describe something about linear equation, an algebraic equation in which each term is a constant or the product of a constant and a single power variable known as Linear equation.Linear equations can have one or more variables.

Popular Posts

System of Linear Equation

A finite set of equation with the variables x 1 , x 2 - - - - -x n is called a System of Linear Equation. a 1 x 1 + a 2 x 2 + - - - - - - + a n x n = b ----------------------- (1) Where a 1, a 2 - - - - - - a n and b are real constants. An equation of this form is called Linear Equation in the variables x 1 , x 2 - - - - - - x n . The variables in a linear equation are sometimes called Unknown. And there are two types of linear equation such as Homogeneous Linear Equation and Non-homogeneous Linear Equation. If b = 0 then (1) is called Homogeneous Linear Equation and if b is not equal 0 the (1) is called Non-homogeneous Linear Equation.

Types of Linear Equation

There are two types of linear equation such as Homogeneous Linear Equation and Non-homogeneous Linear Equation. If b = 0 then (1) is called Homogeneous Linear Equation and if b is not equal 0 the (1) is called Non-homogeneous Linear Equation.

Solution of a System of Linear Equation by Gaussian Elimination

First Step: - Consider the following system of m linear equations (or set of m simultaneous linear equations) in n unknown x 1 , x 2 - - - - - - x n. a 11 x 1 + a 12 x 2 + - - - - - - + a 1n x n = b 1 a 21 x 1 + a 22 x 2 + - - - - - - + a 2n x n = b 2 … …. …. ….. … … .. .. . .. . .. .. . .. .. .. .. . .. System (1) . … . .. .. . .. .. . .. .. . .. . .. . .. .. . .. . .. . .. .. a m1 x 1 + a m2 x 2 + - - - - - - + a mn x n = b m We reduce the System (1) to a simpler system as follows: Step 1: - Elimination of x 1 from the second, third……..mth equations. We may assume that the order (rule) of the equations and the order (rule) of the unknowns in each equation such that a 11 is not equal 0. The variables x 1 can then be eliminated from the second, third ………………..mth equations by subtracting. a 21 /a 11 times the first equation from the second equation a 31 /a 11 times the first equation from the third equation ..