I've attempted to watch the videos on this site, and even though they are more advanced than most stuff around here, I still grasp the concepts roughly. Now I'm doing linear algebra and I'm struggling hard. Just last year I was struggling with calculus before a big exam that might have seen me out of university early, but I watched these videos on Khan Academy and did the exercises and I passed (after maybe a week of thorough practice). In §7.5, he attempts to address the confusion this caused one student who complained, but I would think it better to bother to use set-builder notation and thus to avoid the problem altogether, as do three of the four freely-available linear algebra textbooks recommended by the American Institute of Mathematics (the one that doesn’t omits null spaces entirely).ĭr Grinfeld, and perhaps his students, likely would make fewer mistakes in Gaussian elimination were he to use augmented matrix notation, as is used in the said three textbooks.I've been on Khan Academy for over 3 years now, and this site has saved my ass more than once. §2.12, “Linear Subspaces of the Plane”, is confusing enough that I think it ought to be redone - for now, read the comment under the video.ĭr Grinfeld habitually abuses notation for null spaces, writing a linear combination with unknown coefficients to represent the set of all linear coefficients of its form. I think Dr Grinfeld's linear algebra material is certainly good for its price ($0.00), although my notes from going through the first eight or so chapters note the following small number of issues: There is a website named Lemma run by one Pavel Grinfeld that has a course in linear algebra that is similar to Khan Academy's more developed material, in that it has short lecture videos interspersed with exercises that are graded automatically by the website.

Khan academy algebra linear