Linear Equations
- (Stanford University - Jaclyn Chen)
- Overview
Linear equations are algebraic equations where the highest power of the variable is always one. They are also known as one-degree equations.
Linear equations can be written in the form ax + b = 0 or ax + by + c = 0, where a, b, and c are real numbers and x and y are variables with the highest power one.
Linear equations only have one or two variables. When graphed, a linear equation in one or two variables always represents a straight line. For example, x + 2y = 4 is a linear equation and the graph of this linear equation is a straight line.
The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form.
Linear algebra has algorithms for solving linear equations and systems of linear equations. However, these algorithms have generally a computational complexity that is much higher than the similar algorithms over a field.
[More to come ...]
