diff --git a/content/notes/01-Vector-Spaces-and-Subspaces.md b/content/notes/01-Vector-Spaces-and-Subspaces.md
index 90a2dd677..bfd85cbb8 100644
--- a/content/notes/01-Vector-Spaces-and-Subspaces.md
+++ b/content/notes/01-Vector-Spaces-and-Subspaces.md
@@ -8,6 +8,10 @@ tags:
 
 - ![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 conformm to the eight axioms of scaling and additiveness
+- a vector space is a set whose elements conform to the eight axioms of scaling and additiveness
 - e.g.,
-	- 
\ No newline at end of file
+	- ℝ², ℝ³, P₃
+- In this course we focus on three main vector spaces
+	- ℝⁿ, Pₙ, $M_{m\times n}$ 
+- 
+