UCLA MATH 33A: Linear Algebra and Applications
MATH 33A is UCLA's linear algebra course: systems of equations, matrices, vector spaces, linear transformations, orthogonality, least squares, eigenvalues, and eigenvectors. It's required across engineering, math, and CS, and the linear algebra it teaches underpins machine learning and upper-division applied coursework.
Fennie is independent and not affiliated with UCLA. This is an unofficial study guide.
What makes it hard
Abstraction is the difficulty: vector spaces, bases, and linear independence are a step up from computation, and students who memorize matrix procedures without geometric intuition hit a wall at eigenvalues. The ten-week pace gives little digestion time, and exams test definitions verbatim alongside true/false traps.
What you'll cover
- • Systems of linear equations and matrices
- • Vector spaces and subspaces
- • Linear independence, basis, and dimension
- • Linear transformations
- • Orthogonality and least squares
- • Eigenvalues and eigenvectors
The MATH 33A study guide
How to study for UCLA MATH 33A, step by step.
- 1
Touch the material daily: abstraction arrives fast
On a ten-week quarter, vector spaces and eigentheory get days, not weeks. Twenty minutes daily beats weekend marathons, because linear algebra intuition is built in layers.
- 2
Chase geometric meaning, not just procedures
For every computation (row reduction, projection, eigenvectors) ask what it means geometrically. Students who can picture an eigenvector survive the abstraction wall; pure matrix-arithmetic students don't.
- 3
Learn the definitions verbatim
Span, basis, rank, linear independence, orthogonality: 33A exams test these directly and through true/false traps. State each precisely and produce an example and a counterexample.
- 4
Drill eigenvalues and least squares before the exam
These two topics carry the heaviest exam weight and arrive late in the quarter. Rep them until the computational routine is automatic so exam time goes to the conceptual parts.
Today
Today's MATH 33A plan
What a Fennie Daily Plan looks like for MATH 33A. Yours is built from your own syllabus and adapts every day to your deadlines and progress.
First plan free, no card required. Fennie is independent and unaffiliated with your school.
FAQ
Is MATH 33A hard at UCLA?
It's more abstract than the calculus sequence. Vector spaces and eigentheory are new kinds of thinking, not extensions of old skills, and the quarter gives little digestion time. Students who build geometric intuition early do fine; formula memorizers struggle at eigenvalues.
Do I need MATH 33A for CS at UCLA?
Linear algebra is required for the CS major, and 33A is the standard way to satisfy it. The eigenvalue and least-squares material returns constantly in machine learning and upper-division applied courses, so a solid grade pays off later.
Should I take MATH 33A or 33B first?
They're independent (33A is linear algebra, 33B is differential equations) and students take them in either order. If machine learning is your goal, prioritize 33A earlier; many engineering students take them in adjacent quarters.
More UCLA courses
MATH 31A: Differential and Integral Calculus
MATH 31A is UCLA's first calculus course, covering limits, derivatives, optimization, and the basics of integration, required across engineering, physical science, economics, and life-science-adjacent tracks. Most STEM freshmen take it (or skip it via AP credit) in fall quarter.
MATH 31B: Integration and Infinite Series
MATH 31B covers integration techniques, applications, improper integrals, and infinite sequences and series including Taylor series. It's the second course in UCLA's main calculus sequence and a prerequisite for the multivariable courses that follow.
MATH 32A: Calculus of Several Variables
MATH 32A introduces multivariable calculus: vectors, vector-valued functions, partial derivatives, gradients, and optimization in several variables. It's required for engineering, physics, math, and CS-adjacent tracks, typically taken in the first year after the 31 sequence.
MATH 32B: Calculus of Several Variables
MATH 32B completes UCLA's multivariable calculus sequence: multiple integrals, change of variables, line and surface integrals, and the vector-calculus theorems of Green, Stokes, and Gauss. It follows 32A and is required across engineering and the physical sciences.