From 05153c557d0cc86773f7322929cdc7e2b8f3a7a3 Mon Sep 17 00:00:00 2001
From: ben-jaynes <1btjaynes@gmail.com>
Date: Wed, 7 Oct 2026 10:43:23 -0700
Subject: [PATCH] vault backup: 2026-10-07 10:43:23

---
 College/AU 26/MATH 208 (Matrix Algebra)/Chapter 2.2 - Span.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/College/AU 26/MATH 208 (Matrix Algebra)/Chapter 2.2 - Span.md b/College/AU 26/MATH 208 (Matrix Algebra)/Chapter 2.2 - Span.md
index 9d87276..4ad682a 100644
--- a/College/AU 26/MATH 208 (Matrix Algebra)/Chapter 2.2 - Span.md	
+++ b/College/AU 26/MATH 208 (Matrix Algebra)/Chapter 2.2 - Span.md	
@@ -35,4 +35,6 @@ for the set of vectors $\mathbf{u}_{1}, \mathbf{u}_{2}, \dots, \mathbf{u}_{m}$ i
 This means that $A\mathbf{x}$ is the linear combination of the columns of $A$ where the scalars are the components of the vector $\mathbf{x}$.
 
 This is useful to represent vector equations in a more compact way in the form $A\mathbf{x} = \mathbf{b}$ 
-$$A\mathbf{x}=\mathbf{b} \sim x_{1}\mathbf{a}_{1} + x_{2}\mathbf{a}_{2}+\dots+x_{m}\mathbf{a}_{m}=\mathbf{b} \sim \begin{gather} a_{11}x_{1} + a_{1} \end{gather}$$
\ No newline at end of file
+$$A\mathbf{x}=\mathbf{b} \quad \sim \quad x_{1}\mathbf{a}_{1} + x_{2}\mathbf{a}_{2}+\dots+x_{m}\mathbf{a}_{m}=\mathbf{b} \quad \sim \quad \begin{flalign} a_{11}x_{1} + a_{12}x_{2} + \dots + a_{1m}x_{m} = b_{1} \\ a_{21}x_{1} + a_{22}x_{2} + \dots + a_{2m}x_{m} = b_{2} \\ \vdots \ \\ a_{n1}x_{1} + a_{n2}x_{2} + \dots + a_{nm}x_{m} = b_{n} \end{flalign}$$
+
+if $\mathbf{a}_{1} = \begin{bmatrix}10 \\ 5 \\ 7\end{bmatrix}, \mathbf{a}_{2} = \begin{bmatrix}8 \\ 6 \\ -1\end{bmatrix}, \mathbf{x} = \begin{bmatrix}x_{1} \ x_{2}\end{bmatrix}, \mathbf{b} = \begin{bmatrix}18 \\end{bmatrix}$
\ No newline at end of file