4 files changed, 135 insertions(+), 3 deletions(-)

M README.md
M _layouts/default.html
A multi-variable-calculus/matrices.md
A multi-variable-calculus/vectors.md

@@ 1,10 1,15 @@
 # math
 
-Notes from Scott Druker's calculus classes. Written in a combination of Markdown, HTML, and LaTeX.
+Notes from Bainbridge High School's calculus classes. Written in a combination of Markdown, HTML, and LaTeX.
 
-## AP Calculus
+## Multi-Variable Calculus
+
+### Vectors and Matrices
+- [Vectors, Determinants, and Planes](multi-variable-calculus/vectors.md)
+- [Matrices and Systems of Equations](multi-variable-calculus/matrices.md)
+- Parametric Equations for Curves
 
-[Study Guide (check me out!)](calculus/study-guide.md)
+## AP Calculus
 
 - Limits and Continuity
   - [[2-0] Limits Review](calculus/2-0-limits.md)

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+				{left: "\\(", right: "\\)", display: false},
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 				{left: "$", right: "$", display: false}
 			]});'>
 		</script>

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+---
+layout: default
+---
+
+# Matrices
+
+## Conceptually
+
+## Addition and Subtraction
+Matrices **of the same size** can be added and subtracted together, by adding or subtracting each and every corresponding element.
+
+$$
+\begin{bmatrix}
+2 & 3 & 8\\
+12 & 8 & 5\\
+2 & 9 & 6\\
+\end{bmatrix}
++
+\begin{bmatrix}
+8 & 7 & 1\\
+10 & 19 & 3\\
+7 & 5 & 2\\
+\end{bmatrix}
+=
+\begin{bmatrix}
+10 & 10 & 9\\
+22 & 27 & 8\\
+9 & 14 & 8\\
+\end{bmatrix}
+$$
+
+$$
+\begin{bmatrix}
+2 & 3 & 8\\
+12 & 8 & 5\\
+2 & 9 & 6\\
+\end{bmatrix}
+-
+\begin{bmatrix}
+8 & 7 & 1\\
+10 & 19 & 3\\
+7 & 5 & 2\\
+\end{bmatrix}
+=
+\begin{bmatrix}
+-6 & -4 & 7\\
+2 & -11 & 2\\
+-5 & 4 & 4\\
+\end{bmatrix}
+$$
+
+## Scalar Multiplication
+A matrix can be scaled up or down, by multiplying every element of the matrix by a scalar.
+
+$$
+5
+\begin{bmatrix}
+3 & 6\\
+7 & 9\\
+12 & 3\\
+\end{bmatrix}
+=
+\begin{bmatrix}
+15 & 30\\
+35 & 45\\
+60 & 15\\
+\end{bmatrix}
+$$
+
+## Matrix Multiplication
+Two matrices, of varying size can be multiplied together, by **taking the dot product** of each row of the first and each column of the second.
+
+These matrices must be "
+
+ - that is, **the width of one must be the height of the other**, and vis versa.
+
+The process for this is to multiply each element in each row of the first matrix by each element in each column of the second, and add the results together.
+
+$$Taking\ the\ Dot\ Product$$
+
+$$
+\begin{bmatrix}
+\color{red}{1} & \color{red}{2} & \color{red}{3}\\
+4 & 5 & 6\\
+\end{bmatrix}
+\begin{bmatrix}
+\color{blue}{7} & 8\\
+\color{blue}{9} & 10\\
+\color{blue}{11} & 12\\
+\end{bmatrix}
+=
+\begin{bmatrix}
+\color{purple}{58} & 64\\
+139 & 154\\
+\end{bmatrix}
+$$
+
+$$(1)(7) + (2)(9) + (3)(11) = 58$$
+
+The resulting matrix will have the **height** of the first matrix, and the **width** of the second.
+
+### Non-commutativity
+Matrix multiplication is **not commutative**. $[A][B]$ may $= [C]$, but $[B][A]$ is not obligated to $=[C]$.
+
+### Distributivity
+Although matrix multiplication is non-commutative, it _does_ keep the distributative property.
+
+As
+
+
+
+What $[A][B]$ represents: do transformation $B$, then transformation $A$.
+
+(AB)X = A(BX)

@@ 0,0 1,11 @@
+---
+layout: default
+---
+
+# Vectors, Determinants, and Planes
+
+## Vectors
+
+A **vector** is a quantity that has both a **direction** and a **length**.
+
+## Dot Products