Why People Actually Use MIT OCW for Linear Algebra
Most people come to MIT OpenCourseWare looking for Gilbert Strang's lectures because they need something that explains what a determinant actually means without spending four pages on matrix notation first. The course is free. It's been online since 2001. There are no certificates unless you pay for a separate program through MITx, but you don't need one if you already know how to learn on your own. I ran into a specific problem while going through Problem Set 4 a few years ago. The question asked you to verify that Ax = b has no solution for a particular 3x3 system, then pivot the matrix to show exactly where the inconsistency appears. The OCW solutions posted on the site work through the arithmetic step by step, but they skip the part about why row 3 becomes [0 0 0 | 5] instead of [0 0 0 | 0]. I had to pause the video, re-read the relevant chapter on elimination, and then manually redo the pivot on paper to see that the third equation was literally saying 0 equals 5. Once I understood that, the rest of the problem set clicked into place. The workaround was just slow, deliberate pencil work paired against the video, not speed. I spent about forty-five minutes on that single problem. The official solution video is seventeen minutes long and covers about six problems. The lectures are available in two main formats: the full classroom recordings from MIT's actual course 18.06, and the supplementary problem-solving sessions where Strang works through homework questions. Both are hosted directly on the MIT OpenCourseWare website. You can find them at ocw.mit.edu/courses/18-06-linear-algebra-spring-2010. Everything is downloadable as MP4 or viewable in a browser. There are also PDF lecture notes, exams with solutions, and handouts scattered across the course page.
Downloading Mit Open Courseware Linear Algebra Materials
MIT doesn't provide a single zip file. You have to grab things individually, which is why I keep a folder on my machine organized by topic. Here's the structure I use, and it saves me from browsing around every time I need a specific resource. Create folders for Lectures, Problem Sets, Exams, and Notes. Download the video files from the lectures section. Each lecture has a "Video" link that opens a page with an MP4 download button. The problem sets are in the Assignments section. Each PDF contains both the problems and the solutions. Some semesters separate them into two files, some combine them. Check the date on the PDF to know which version you're looking at. The exams are the most useful resource if you want to test yourself. There are two midterm exams and a final, each with full solutions. I used the midterm from 2006 to check my understanding after finishing the first twelve lectures. I timed myself for eighty minutes, which is the actual exam length. I scored twenty-eight out of fifty. That told me I was okay on row reduction but completely lost on eigenvalues and singular value decomposition. I went back and rewatched lectures nineteen through twenty-two.
If you want everything at once, there's no official bundle, but people have uploaded videos to YouTube that cover the entire semester. Search for "Gilbert Strang full course linear algebra" and you'll find a channel that has all thirty-five lectures in order. The video quality is lower than the OCW downloads, and the audio sometimes has classroom noise, but it's fine if you're watching on a second monitor while working.
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What the Course Actually Covers
Linear algebra is twelve chapters long if you count the appendices. The core material runs from Chapter 1 through Chapter 9. Everything after that is applications or advanced topics. If you only have time for one pass, stop at Chapter 9. That covers elimination, vector spaces, orthogonal projections, determinants, eigenvalues, and positive definite matrices. The remaining chapters on Markov matrices, Fourier transforms, and the singular value decomposition are important but not strictly necessary for most practical work. Strang's approach is unusual compared to a textbook-driven course. He introduces subspaces early, in the second lecture, right after he explains how to solve Ax equals b. Most courses wait until after two or three chapters on determinants. The reason this matters is that you end up understanding why rank deficiency is a geometric property, not just an algebraic one. A matrix with fewer pivots than columns isn't just "invertible or not." It's a projection onto a lower-dimensional space, and you see that immediately. One thing beginners consistently miss: the connection between the four fundamental subspaces and elimination is not obvious until you've done it three or four times. Strang puts it in Chapter 3, and he draws the diagram that shows how the null space, column space, row space, and left null space relate to each other through transpose operations. I kept skipping that diagram because it looked like extra work. After the second midterm, I realized I was making the same mistake on orthogonal complement questions because I hadn't internalized that the left null space is the orthogonal complement of the column space. The fix was simple. I redrew the four-subspace diagram from memory on a blank sheet of paper and taped it to my wall. Every time I opened my notebook, I saw it. Within two weeks, I stopped second-guessing those questions.
Problem-Solving Workflow That Actually Works
Don't watch the lectures passively. Strang moves fast, and the pace assumes you're working problems alongside him. If you just sit and watch, you'll finish a twenty-minute lecture with a false sense of understanding. The gap between watching and doing is where most people fall apart. Here's the routine I used, and it took me about three hours per lecture to complete properly. First, read the corresponding chapter in Strang's free online textbook, which is linked directly from the OCW page. You don't have to read cover to cover. Skim the examples and focus on the sections that match the lecture topics. Then watch the lecture. Pause after each example and try the calculation yourself before he reveals the answer. Next, do the problem set assigned for that week. The OCW problem sets are available as PDFs with solutions at the end. Do the problems without looking at the solutions first. If you get stuck, spend fifteen minutes maximum before checking the solution. When you check it, don't just read it. Write out the full solution on paper as if you were turning it in, because that's how you catch the arithmetic mistakes you're making. I found that writing everything by hand, not on a laptop, made a difference. Typing matrices is annoying. Handwriting forces you to slow down and notice when a row operation produces a fraction you didn't expect. I also kept a separate notebook for the "aha" moments. Not the theorems. The moments where a concept finally connected to something you already knew. That notebook became my review document before exams.
There's a counter-intuitive point about determinants that trips people up. You don't need to compute determinants to solve most linear algebra problems, and Strang makes this clear in Chapter 3. But people keep computing them anyway because they learned to from high school or a different textbook. Determinant-based methods like Cramer's rule are computationally expensive and numerically unstable for anything larger than a 3x3 matrix. If you're solving a system of equations in practice, use elimination or a numerical solver. The determinant is useful for theoretical questions and for checking whether a matrix is invertible, but it's not a tool you reach for repeatedly. Another thing people miss is that the geometric interpretation of eigenvalues and eigenvectors is easier to grasp before you learn the characteristic polynomial. Strang shows this in Lecture 37, which is actually beyond the core curriculum but worth watching. An eigenvector is a direction that doesn't change when you multiply by the matrix. The eigenvalue tells you how much that direction stretches. If you visualize this before you start crunching characteristic polynomials, the algebra becomes less abstract. I found it helpful to sketch the transformation on graph paper for a 2x2 matrix before doing any calculations. The sketch didn't have to be precise. It just had to show which way the axes were moving.
Known Gaps and Where This Course Falls Short
MIT OpenCourseWare Linear Algebra is excellent for theory and conceptual understanding, but it has limitations you should know about before committing to it as your sole resource. The first gap is computational practice. The problem sets are mathematics problems, not programming or numerical computation problems. If you're studying linear algebra to use it in machine learning, data science, or engineering simulation, you'll need supplemental work. The OCW course won't teach you how to implement matrix operations in Python or how to use NumPy effectively. Strang mentions MATLAB occasionally, but the course is not a programming course. I supplemented this with a separate online module on numerical linear algebra, specifically Golub and Van Loan's approach to matrix factorizations. That took about six weeks alongside the OCW material. The second gap is that the course assumes a level of mathematical maturity that most undergraduates haven't fully developed. The proofs are rigorous but compact. If you're struggling with the jump from concrete matrix arithmetic to abstract vector space arguments, you might need a more scaffolded resource. Strang's textbook, Introduction to Linear Algebra, is quite good at bridging this gap, but even it can feel dense if you haven't seen formal proofs before. I knew someone who dropped out of the OCW course halfway through because the transition from elimination to abstract vector spaces felt like a different subject. They came back after reading Chapter 1 of the textbook twice and rewatching the first five lectures. It worked, but it cost them roughly two weeks of recovery time.
A third limitation is that some of the older lectures have audio issues. The 2010 recording is the best preserved, but a few lectures in the later part of the semester have microphone dropouts or classroom chatter that makes certain sections hard to follow. Lecture 28, which covers Gram-Schmidt orthogonalization, has a section around the twelve-minute mark where the audio cuts out for about forty seconds. You can usually infer what he's saying from the whiteboard, but it's frustrating. I kept a transcript PDF from an older semester for reference and switched to that when the audio was unreliable. There's also no interactive component. You can't ask questions on the OCW platform, and there's no discussion forum tied directly to the course. People who benefit from asking questions or getting feedback on their problem sets may find this isolating. The MITx version offers more structure, including verified certificates and some discussion features, but it costs money. If you're self-directed and comfortable working through problems without external validation, the free OCW version is sufficient. If you need accountability or peer interaction, consider pairing it with an online community like Reddit's r/learnmath or a study group.
How Long This Actually Takes
A complete run-through of the core 18.06 course, including all lectures, problem sets, and exams, takes approximately forty to fifty hours of focused work. That's about twelve weeks at a pace of three to four hours per week, which matches MIT's undergraduate schedule. If you're working full-time and studying part-time, plan for sixteen to twenty weeks. The course is designed so that each lecture corresponds to one week of class time, so following that rhythm helps you pace yourself. The problem sets are the time sink. Each one takes between one and three hours depending on your familiarity with the material. I found that the first four problem sets were straightforward and took about an hour each. Problem Set 5, which covers eigenvalues, took me three hours because I was still getting comfortable with the characteristic polynomial method. Problem Set 9, on positive definite matrices, took me two hours and required me to revisit the section on quadratic forms from the textbook. Don't underestimate the later problem sets. They build on everything that came before, and if you have gaps from earlier weeks, they'll pile up quickly. The exams are the best indicator of whether you're ready to move on. If you score above seventy percent on a timed midterm, you're in good shape. Below sixty, go back and review the relevant lectures. I scored forty-eight on my first attempt at the midterm on eigenvalues and singular values. I spent a week rewatching lectures 30 through 35 and redoing Problem Sets 7 through 9 before retaking the exam. I scored seventy-two the second time. The material hadn't changed. My understanding had.
If your goal is simply to understand the concepts for a job interview or a self-study project, you don't need to complete every problem set. Focus on the lectures, do the first eight problem sets, and take the two midterms under timed conditions. That gives you about eighty percent of the course's value in roughly half the time.
