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+.EQ
+delim $$
+.EN
+.TL
+Linear Algebra Introduction
+.AU
+Preston Pan
+.AI
+Pacific School of Science and Inquiry
+
+.PP
+Linear algebra is a subject that is worthy of studying if you are looking
+to analyze data in any systematic way, or if you are attempting to represent
+multidimensional (or multivariable) quantities in a structured way.
+Therefore, everyone in STEM and even in the social sciences should know about
+linear algebra and a little bit of the mathematical theory behind it.
+
+.PP
+I will be introducing subjects regarding linear algebra from the perspective
+of physics, though you do not need to know much physics in order to understand
+most of my explanations.
+
+.PP
+You might know that in high school physics, all the equations are introduced
+as one dimensional equations (that is to say, most equations that are introduced
+only work if the object or objects in question only move forwards and backwards,
+or any other singluar direction). Of course, in real life, there are at least
+three spatial dimensions, so one dimensional equations just won't model real
+life well. In these scenarios, it is useful to consider linear algebra as a
+systematic way to represent direction and motion in three dimensions. With
+this motivation, we start investigating.
+
+.PP
+One way we can represent two dimensional space is with a coordinate system. For
+example, we can have a point $(3, 2)$ which represents a single point three
+units right and two units up in a coordinate system.
+
+.G1
+coord x 0, 11 y 0, 11
+3 2
+"(3, 2)" above at 3,2
+.G2
+
+.PP
+Now, let's imagine that this point $(3, 2)$ represents a force in a certain direction.
+For example, we can draw a line from the origin to this point and the resulting force's
+magnitude will be represented by the length of the line in question (which can be obtained
+via the pythagorean theorem).
+
+.G1
+draw solid
+coord x 0, 11 y 0, 11
+0 0
+3 2
+"(3, 2)" above at 3,2
+"$sqrt {3 sup 2 + 2 sup 2}$" above at 1,2
+.G2