Math 111 is UBC's introduction to matrix algebra—also called linear algebra—covering systems of equations, matrices, vectors, and determinants. It's a foundational course for engineering, computer science, physics, and many science programs. Unlike calculus, which deals with continuous change, linear algebra focuses on solving systems, transforming spaces, and understanding structures. Many students find Math 111 conceptually different from high school math: it's abstract, proof-heavy, and requires thinking in higher dimensions. But with the right approach, the patterns become clear and the power of linear algebra reveals itself.
What is covered in UBC Math 111?
Math 111 introduces matrix algebra with applications to science and engineering. Topics include:
- Systems of linear equations: Solving using Gaussian elimination, row reduction, and echelon forms
- Matrices: Operations (addition, multiplication, transpose), properties, and special types (identity, inverse, diagonal)
- Determinants: Calculating determinants, properties, and applications to invertibility
- Vector spaces: Understanding \(\mathbb{R}^n\), subspaces, span, and linear combinations
- Linear independence: Determining whether sets of vectors are independent or dependent
- Basis and dimension: Finding bases for vector spaces and understanding dimensionality
- Linear transformations: Functions between vector spaces and their matrix representations
- Eigenvalues and eigenvectors: Characteristic polynomials, diagonalization, and applications
Math 111 is typically taken alongside or after Math 100/101 and is required for many engineering, computer science, and science programs.
Common challenges students face in Math 111
Abstract thinking replaces computation
High school math is mostly about calculating answers. Linear algebra asks you to think about spaces, transformations, and structures. The shift from computational to conceptual thinking is difficult.
Notation and terminology
Terms like "span," "linear independence," "kernel," and "nullspace" pile up quickly. If you don't keep up with definitions, the course becomes incomprehensible.
Proof-based questions
Exams often ask you to prove whether something is true or false. If you're not used to writing mathematical arguments, these questions feel daunting.
Eigenvalues and diagonalization
The second half of the course introduces eigenvalues and eigenvectors, which feel abstract and computational at the same time. Many students struggle to understand what these concepts mean and why they matter.
How Learn4Less helps you succeed in Math 111
Our tutors specialize in first-year linear algebra and understand exactly where students get stuck.
Conceptual clarity
We explain abstract concepts with visual intuition and concrete examples. You'll understand what span means, why linear independence matters, and how determinants relate to geometry.
Step-by-step problem solving
From row reduction to finding eigenvalues, we walk you through problems systematically. You'll learn efficient techniques and how to avoid common mistakes.
Proof strategies
We teach you how to approach proof-based questions: how to start, what definitions to use, and how to structure your arguments clearly.
Math 111 exam and midterm preparation
Math 111 typically has two midterms and a final exam. Here's how we prepare you:
Practice with past exams
We work through previous years' exams so you know what question types to expect. You'll practice computational problems, proofs, and conceptual questions.
Eigenvalue and diagonalization focus
These topics appear heavily on exams. We drill you on finding eigenvalues, eigenvectors, and determining when matrices are diagonalizable.
Time management
Linear algebra problems can be time-consuming. We teach you how to allocate time efficiently and which problems to prioritize.
Why choose Learn4Less for Math 111 tutoring?
First-year specialization
We focus on UBC's first-year math courses, including linear algebra. Our tutors have guided hundreds of Math 111 students successfully.
Experience with UBC curricula
We know UBC's Math 111 syllabus, textbook (often *Linear Algebra and Its Applications* by Lay), and exam formats. We tailor our sessions to what UBC professors emphasize.
Flexible formats
Choose in-person tutoring near UBC or online sessions with screen sharing. Need help before a specific midterm? Book a targeted prep session. Want ongoing support? Weekly tutoring keeps you on track.
Video study packages
Prefer self-paced learning? Our video packages cover key Math 111 topics—perfect for reviewing before exams.
Frequently Asked Questions
What's the difference between Math 111 and Math 152?
Math 111 is a one-term course covering the basics of matrix algebra for engineering and science students. Math 152 is a more advanced linear systems course, often focusing on applications to differential equations and computing. Check your program requirements to see which one you need.
Do I need to take Math 100 before Math 111?
Not always. Math 111 is mostly independent of calculus, though some examples use derivatives. Check your program's requirements, but many students take Math 111 and Math 100 concurrently.
Is Math 111 harder than Math 100?
They're different. Math 100 is about rates of change and optimization. Math 111 is about systems, structures, and abstract thinking. Some students find linear algebra harder because it's less intuitive; others find it easier because it's more systematic.
How much of Math 111 is proofs versus computation?
It depends on your professor, but typically 30-40% of exam questions involve proofs or conceptual explanations. You can't succeed by just memorizing procedures—you need to understand the concepts.
When should I get a tutor for Math 111?
As soon as you feel confused by the abstract concepts or fall behind on problem sets. Linear algebra builds quickly, and falling behind makes catching up very difficult. Proactive tutoring from the start is the best strategy.