## ~j-james/math

5d4afdeacf29729bb390e036077786696323021b — j-james 2 years ago
Fix broken LaTex

Also, throw in vector and matrices draft notes

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

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

M README.md => README.md +8 -3
@@ 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)


M _layouts/default.html => _layouts/default.html +2 -0
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<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" crossorigin="anonymous"
{left: "$$", right: "$$", display: true},
+				{left: "\$$", right: "\$$", display: false},
+				{left: "\$", right: "\$", display: true},
{left: "$", right: "$", display: false}
]});'>
</script>


A multi-variable-calculus/matrices.md => multi-variable-calculus/matrices.md +114 -0
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+---
+layout: default
+---
+
+# Matrices
+
+## Conceptually
+
+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)


A multi-variable-calculus/vectors.md => multi-variable-calculus/vectors.md +11 -0
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+---
+layout: default
+---
+
+# Vectors, Determinants, and Planes
+
+## Vectors
+
+A **vector** is a quantity that has both a **direction** and a **length**.
+
+## Dot Products