From 7434c516a70f3b6b40bc6255b6697ea2680cd0f2 Mon Sep 17 00:00:00 2001
From: ben-jaynes <1btjaynes@gmail.com>
Date: Tue, 6 Oct 2026 11:45:34 -0700
Subject: [PATCH] vault backup: 2026-10-06 11:45:34

---
 .../Chapter 2.1 Notes.md                      | 31 +++++++++++++++++--
 1 file changed, 29 insertions(+), 2 deletions(-)

diff --git a/College/AU 26/MATH 208 (Matrix Algebra)/Chapter 2.1 Notes.md b/College/AU 26/MATH 208 (Matrix Algebra)/Chapter 2.1 Notes.md
index ad1d85e..36d7d13 100644
--- a/College/AU 26/MATH 208 (Matrix Algebra)/Chapter 2.1 Notes.md	
+++ b/College/AU 26/MATH 208 (Matrix Algebra)/Chapter 2.1 Notes.md	
@@ -1,7 +1,34 @@
 #uw/notes #uw/class/math208 
 - - -
-Vectors can be represented vertically in a matrix:
-$$u = \begin{bmatrix}
+Vectors can be represented vertically in a matrix (column vector):
+$$\mathbf{u} = \begin{bmatrix}
 u_{1} \\ u_{2} \\ \vdots \\ u_{n}
 \end{bmatrix}$$
 
+
+> [!NOTE] Basic Properties
+> if 
+
+if $\mathbf{u}$ and $\mathbf{v}$ are vectors defined as 
+$$\mathbf{u} =\begin{bmatrix}
+u_{1} \\ u_{2} \\ \vdots \\ u_{n}
+\end{bmatrix} \quad \text{and} \quad \mathbf{v} =\begin{bmatrix}
+v_{1} \\ v_{2} \\ \vdots \\ v_{n}
+\end{bmatrix}$$
+
+**Equality:**
+$\mathbf{u}=\mathbf{v}$ if and only if $u_{1}=v_{1}, u_{2}=v_{2},\dots,u_{n}=v_{n}$
+**Addition:**
+$$\mathbf{u}+\mathbf{v} = \begin{bmatrix}
+u_{1} \\ u_{2} \\ \vdots \\ u_{n}
+\end{bmatrix} + \begin{bmatrix}
+v_{1} \\ v_{2} \\ \vdots \\ v_{n}
+\end{bmatrix} = \begin{bmatrix}
+u_{1}+v_{1} \\ u_{2}+v_{2} \\ \vdots \\ u_{n}+v_{n}
+\end{bmatrix}$$
+**Scalar Multiplication:**
+$$c \mathbf{u} = c \begin{bmatrix}
+u_{1} \\ u_{2} \\ \vdots \\ u_{n}
+\end{bmatrix} = \begin{bmatrix}
+c \cdot u_{1} \\ c \cdot u_{2} \\ \vdots \\ c \cdot u_{n}
+\end{bmatrix}$$