A linear equation is an algebraic equation that contains only linear terms, meaning that the variables are raised to the first power and are not multiplied or divided by each other. The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
The span of a set of vectors is the set of all possible linear combinations of those vectors. In other words, it is the set of all vectors that can be created by multiplying each vector in the set by a scalar and adding them together.
A system of linear equations can be solved by using various methods such as substitution, elimination, or graphing. The goal is to find the values of the variables that satisfy all of the equations in the system.
A vector is a mathematical object that has both magnitude (size) and direction. It is represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude. Vectors can be added, subtracted, and multiplied by scalars.
Linear equations are used in many real-life situations, such as calculating the speed of an object, determining the cost of a product based on the number of units sold, or predicting future values based on past trends. They are also used in fields like physics, engineering, and economics to model and solve various problems.