From 5746e06fb136ecb3853dd70d4fe05f2cf1685cb1 Mon Sep 17 00:00:00 2001
From: ben-jaynes <1btjaynes@gmail.com>
Date: Thu, 28 May 2026 00:20:53 -0700
Subject: [PATCH] vault backup: 2026-05-28 00:20:53

---
 Wiki/Math/Determinite of a Matrix.md           |  0
 Wiki/Math/Matricies/Determinant of a Matrix.md | 10 ++++++++++
 Wiki/Math/Vector Basics.md                     |  2 ++
 3 files changed, 12 insertions(+)
 delete mode 100644 Wiki/Math/Determinite of a Matrix.md
 create mode 100644 Wiki/Math/Matricies/Determinant of a Matrix.md

diff --git a/Wiki/Math/Determinite of a Matrix.md b/Wiki/Math/Determinite of a Matrix.md
deleted file mode 100644
index e69de29..0000000
diff --git a/Wiki/Math/Matricies/Determinant of a Matrix.md b/Wiki/Math/Matricies/Determinant of a Matrix.md
new file mode 100644
index 0000000..a8f4586
--- /dev/null
+++ b/Wiki/Math/Matricies/Determinant of a Matrix.md	
@@ -0,0 +1,10 @@
+For a 2 x 2 matrix:
+$$ \det\begin{pmatrix}
+a&b\\c&d
+\end{pmatrix} = \begin{vmatrix} a&b\\c&d\end{vmatrix} = ad-bc$$
+For a 3 x 3 matrix:
+$$\begin{vmatrix} a&b&c\\d&e&f\\g&h&i\end{vmatrix} = a\begin{vmatrix} e&f\\h&i\end{vmatrix} - b\begin{vmatrix} d&f\\g&i\end{vmatrix} + c\begin{vmatrix} d&e\\g&h\end{vmatrix} = a(ei-hf)-b(di-gf)+c(dh-ge)$$
+### Properties
+$$\begin{matrix}
+a&b\\a&b
+\end{matrix}$$
\ No newline at end of file
diff --git a/Wiki/Math/Vector Basics.md b/Wiki/Math/Vector Basics.md
index 35a044d..4445f92 100644
--- a/Wiki/Math/Vector Basics.md	
+++ b/Wiki/Math/Vector Basics.md	
@@ -22,6 +22,8 @@ Used to find the vector of magnitude 1 in the same direction as $u$
 $$a \times b = \begin{vmatrix} i&j&k\\a_1&a_2&a_3\\b_1&b_2&b_3\end{vmatrix}= i(a_2b_3-a_3b_2)-j(a_1b_3-a_3b_1)+k(a_1b_2-a_2b_1)$$
 Used to create a vector that is orthogonal to both $a$ and $b$. To find what direction it will point in use the right-hand rule (thumb, pointer and middle finger).
 
+The cross product is calculated by finding the [[Determinant of a Matrix|determinant]] of the matrix formed in the equation above with the unit vectors in the top row.
+
 Properties:
 - Not commutative $$u\times v \ne v \times u$$
 - Anti-commutative $$ u \times v = -(v \times u) $$