Linear algebra and multivariable calculus practice exercises for khan-academy videos?

Question

I have completed linear algebra in khan-academy and I am going to watch the multivariable calculus lectures from there .There is no exercise in the linear algebra section. And I heard that linear algebra and multivariable calculus is the different way of looking at the same thing ,

so I am seeking for some practice exercises(possibly worked out so that I can check my soln) so that both my linear algebra skill and intuition behind the relation multivariable calculus become strengthen. Thanks in advance

Answer 1

There are problems and solutions in this course:

http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/index.htm

See under the different units.

Answer 2

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.

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:

1. §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.

2. Dr 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. 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).

3. Dr 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.

Answer 3

For something not similar to Khan Academy, a different answer is provided by the free textbooks recommended by the American Institute of Mathematics that I referenced in my other answer. Of the four free linear algebra textbooks that they recommend, three have exercises with solutions:

• Linear Algebra by Jim Hefferon — This textbook won the 2020 Daniel Solow Author's Award of the Mathematical Association of America, and the award citation specifically notes (among other worthy qualities) the book's “tremendous variety of exercises”, so this book may be a particularly appropriate choice.

• A First Course in Linear Algebra by Rob Beezer

• Linear Algebra Done Wrong by Sergei Treil