From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 29 Jan 2019 01:24:09 +0000 (+1100)
Subject: linear dependence of vectors (spec)
X-Git-Tag: yr12~276
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/139316a2f1962263e113aff0a9ef24c90ea64aeb

linear dependence of vectors (spec)
---

diff --git a/spec/vectors.md b/spec/vectors.md
index 2374b2a..6218b24 100644
--- a/spec/vectors.md
+++ b/spec/vectors.md
@@ -142,6 +142,13 @@ Useful vector properties:
 - Two vectors $\boldsymbol{a}$ and $\boldsymbol{b}$ are perpendicular if $\boldsymbol{a} \cdot \boldsymbol{b}=0$
 - $\boldsymbol{a} \cdot \boldsymbol{a} = |\boldsymbol{a}|^2$
 
+## Linear dependence
 
+Vectors $\vec{a}, \vec{b}, \vec{c}$ are linearly dependent if they are non-parallel and:
 
+$$k\vec{a}+l\vec{b}+m\vec{c} = 0$$
+$$\therefore \vec{c} = m\vec{a} + n\vec{b} \quad \text{(simultaneous)}$$
 
+$\vec{a}, \vec{b},$ and $\vec{c}$ are linearly independent if no vector in the set is expressible as a linear combination of other vectors in set, or if they are parallel.
+
+Vector $\vec{w}$ is a linear combination of vectors $\vec{v_1}, \vec{v_2}, \vec{v_3}$