diff --git a/content/notes/01-Vector-Spaces-and-Subspaces.md b/content/notes/01-Vector-Spaces-and-Subspaces.md
index bfd85cbb8..7ab43a90c 100644
--- a/content/notes/01-Vector-Spaces-and-Subspaces.md
+++ b/content/notes/01-Vector-Spaces-and-Subspaces.md
@@ -6,12 +6,14 @@ tags:
 - math202
 ---
 
-- ![pdf](https://www.maths.otago.ac.nz/webdata/resources/math202/2022_S2_Outline_Notes/Ch1.pdf?m=1657334841)
+- [pdf](https://www.maths.otago.ac.nz/webdata/resources/math202/2022_S2_Outline_Notes/Ch1.pdf?m=1657334841)
 
 - a vector space is a set whose elements conform to the eight axioms of scaling and additiveness
 - e.g.,
 	- ℝ², ℝ³, P₃
 - In this course we focus on three main vector spaces
 	- ℝⁿ, Pₙ, $M_{m\times n}$ 
+
+- a vector subspace is a subset of a vector space whose elements (which are vectors) are additively and multipicatively closed and contain the zero vector
 -