What is Linear Algrebra?

To understand what Linear Algebra is, first we should understand what a linear equation is. A linear equation is an equation where each value includes no exponentiation (other than $1$) and isn't passed into any functions. For example: $$ x + y + z = 0 $$ $$ a + b + c + d + e = 54 $$ Examples of equations that are not linear include: $$ x^2 + y = 3 $$

$$ sin(x) + log(y) = 13 $$

And what linear algebra is is a way for us to solve variables for sets of linear equations. By leveraging it, we can more quickly and efficiently solve problems pertaining to computer graphics, electrical engineering, or what we will be using it for, data science and artificial intelligence.
This is done by following a pretty simple equation: $$ M * w = v $$ Where $M$ is a matrix, $w$ is a vector holding our variables in a set of linear equations, and $v$ is a vector holding the answers to our set of linear equations.

Vectors

A vector is an object that both has a magnitude as well as a direction. It can be denoted in boldface or with a arrow over the name such as $\textbf{a}$ or $\overrightarrow{a} \ $. The magnitude of a vector is how much it moved, and can be denoted like so: $||\textbf{a}||$.