# Course - Linear Algebra MT22

> Source: https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/ · Updated: 2025-09-30 · Tags: uni, course

> The first algebra course of the degree, serving as an introduction to linear algebra. Linear algebra is the branch of mathematics concerned with concepts like vectors and linear maps.
> 
> 
> This course dealt specifically with the basic definitions of a vector space, bases, linear maps and matrices.

- [Course Webpage](https://courses.maths.ox.ac.uk/course/view.php?id=609)
- [Lecture Notes](https://courses.maths.ox.ac.uk/pluginfile.php/25471/mod_folder/content/0/lecture_notes22.pdf)
- Other linear algebra courses:
	- [Course - Linear Algebra II HT23](https://ollybritton.com/notes/uni/prelims/ht23/linear-algebra/)
	- ...and in part A, the theme continues with:
	- [Course - Linear Algebra MT23](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/)
- Other courses this term: [Courses MT22](https://ollybritton.com/notes/uni/prelims/mt22/)

### Notes
- [Notes - Linear Algebra I MT22, Chapter 1](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/chapter-1/)
- [Notes - Linear Algebra I MT22, Chapter 2](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/chapter-2/)
- [Notes - Linear Algebra I MT22, Chapter 3](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/chapter-3/)
- [Notes - Linear Algebra I MT22, Chapter 4](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/chapter-4/)
- [Notes - Linear Algebra I MT22, Chapter 5](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/chapter-5/)
	- [Notes - Linear Algebra I MT22, Steinitz Exchange Lemma](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/steinitz-exchange-lemma/)
	- [Notes - Linear Algebra I MT22, Dimension Formula](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/dimension-formula/)
- [Notes - Linear Algebra I MT22, Chapter 6](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/chapter-6/)
	- [Notes - Linear Algebra I MT22, Rank-Nullity Theorem](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/rank-nullity-theorem/)
	- [Notes - Linear Algebra I MT22, Rank and nullity inequalities](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/rank-and-nullity-inequalities/)
- [Notes - Linear Algebra I MT22, Chapter 7](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/chapter-7/)
	- [Notes - Linear Algebra I MT22, Change of basis theorem](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/change-of-basis-theorem/)
	- [Notes - Linear Algebra I MT22, Column rank and row rank](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/column-rank-and-row-rank/)
- [Notes - Linear Algebra I MT22, Chapter 8](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/chapter-8/)
	- [Notes - Linear Algebra I MT22, Cauchy-Schwarz Inequality](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/cauchy-schwarz-inequality/)
	- [Notes - Linear Algebra I MT22, Triangle Inequality](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/triangle-inequality/)
- [Notes - Linear Algebra MT22, Misc](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/notes/misc/)

### Lectures
- [Lecture - Linear Algebra MT22, I](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/1/)
- [Lecture - Linear Algebra MT22, II](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/2/)
- [Lecture - Linear Algebra MT22, III](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/3/)
- [Lecture - Linear Algebra MT22, IV](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/4/)
- [Lecture - Linear Algebra MT22, V](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/5/)
- [Lecture - Linear Algebra MT22, VI](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/6/)
- [Lecture - Linear Algebra MT22, VII](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/7/)
- [Lecture - Linear Algebra MT22, VIII](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/8/)
- [Lecture - Linear Algebra MT22, IX](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/9/)
- [Lecture - Linear Algebra MT22, X](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/10/)
- [Lecture - Linear Algebra MT22, XI](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/11/)
- [Lecture - Linear Algebra MT22, XII](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/12/)
- [Lecture - Linear Algebra MT22, XIII](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/13/)
- [Lecture - Linear Algebra I MT22, XIV](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/14/)

### Problem Sheets
- [Sheet 1](https://courses.maths.ox.ac.uk/pluginfile.php/25472/mod_assign/introattachment/0/Sheet1.pdf?forcedownload=1) (on lectures 1 and 2)
- [Sheet 2](https://courses.maths.ox.ac.uk/pluginfile.php/25473/mod_assign/introattachment/0/Sheet2.pdf?forcedownload=1) (on lectures 3 and 4)
- [Sheet 3](https://courses.maths.ox.ac.uk/pluginfile.php/25474/mod_assign/introattachment/0/Sheet3.pdf?forcedownload=1) (on lectures 5 and 6)
- [Sheet 4](https://courses.maths.ox.ac.uk/pluginfile.php/25475/mod_assign/introattachment/0/Sheet4.pdf?forcedownload=1) (on lectures 7 and 8)
- [Sheet 5](https://courses.maths.ox.ac.uk/pluginfile.php/25476/mod_assign/introattachment/0/Sheet5.pdf?forcedownload=1) (on lectures 9 and 10), [Problem Sheet - Linear Algebra MT22, V](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/sheets/5/)
- [Sheet 6](https://courses.maths.ox.ac.uk/pluginfile.php/25477/mod_assign/introattachment/0/Sheet6.pdf?forcedownload=1) (on lectures 11 and 12)
- [Sheet 7](https://courses.maths.ox.ac.uk/pluginfile.php/25478/mod_assign/introattachment/0/Sheet7.pdf?forcedownload=1) (on lectures 13 and 14)

### Proofs
- [Proofs - Linear Algebra I MT22](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/proofs/)

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