MAT1503 → Linear Algebra

One does not Simply pass Linear Algebra

Real Talk 💬

Cut the sugar-coating.
If you do not work through the textbook, practice relentlessly, and work with other sources, you will
probably fail.
And not to throw shade — but when I took MAT1504, the module was poorly run, with:

  1. Late marked Assignments/Sections unmarked.
  2. Error-riddled questions.
  3. Weak and Unresponsive administration
  4. Exams that focused more on theory and practical application

With all of that said, THIS IS AN INCREDIBLE SUBJECT OF STUDY

What is Linear Algebra Really? 🤔

I could give you the textbook definition:

Linear Algebra studies vectors, matrices, linear transformations, and vector spaces. It's used to solve
systems of linear equations and model real-world linear relationships.

But let me give it to you Straight

Linear Algebra is the math of straight lines — and everything that can be broken down into
combinations of straight lines

That might sound basic — but it is everywhere!
In my own experience, I have used Linear Algebra for:

  1. 1. Game Development (movement, graphics, and collision detection) to name a few applications of LA
  2. 2. Algorithm Design (especially in Numerical Analysis...3rd year module)

Core Topics You’ll Cover 📚:

🧾 Systems of Linear Equations & Matrices
Understand what a linear equation is and how a matrix can represent multiple equations at once.

Determinants 🔢
A single number that tells you a lot about a matrix:

  1. For you the Novice determinants are easily calculated but difficult to interpret
  2. Is it invertible
  3. Does it stretch or squash space

Euclidean Vector Spaces 📏
A combination of high school geometry and vector math — mostly spatial reasoning in 2D and 3D.

General Vector Spaces 🌀
Same ideas, but now we remove visuals and generalize. It gets more abstract. You'll need to reason without diagrams.

Complex Numbers ⚡
The GOAT topic, my favourite. If you understand how to take the root of (-1), you are halfway there.

Final Thoughts 🧠

Exam Strategy 🧪:

  • MCQ (Multiple Choice) format — no partial marks (This is assuming the format is the same since 2022)
  • Practice past exams under time pressure (Exams prior to the McQ where easier because they were written and had little/no errors but practice both types)
  • Expect trick questions, especially on theory (Is a trick question a mark of a smart or stupid professor?)
  • Get used to writing quick matrix operations and interpreting abstract vector statements (Goodluck calculating the determinant of a 5x5 matrix)

I love Linear Algebra, I let this module and the admin break me.
Do not let that happen to you, make sure you do well in the assignments, it will greatly consolidate and prepare you for exams.

Final Advice 🎓:
LA is not impossible, but it is unforgiving.
There are students who have failed multiple times.
If you slack early, it will show.
✅ Do every exercise in the textbook
✅ Watch YouTube walkthroughs (especially 3Blue1Brown for vector intuition)
✅ Treat this like a practical module, even if the assignments don't

Helpful Links 🔗

Introduction to LA
Linear Algebra for Computer Scientists
Why is Linear Algebra useful?
Complex Numbers - Basics