This is the first draft of my linear algebra lecture notes. It will have to go through one or two more iterations before it becomes respectable. However I post it here, mainly for my students and for anyone else interested.
I am planning to use these notes during mu summer course. There are many differences from the usual way I handled the course before,
(1) I have tried to keep the content minimal and essential,
(2) The problems are somewhat open ended in the sense students are required to construct a part of the problem themselves which is much more fun.
A nice example is the following. One of the problem asks students to create 3 lines with a unique intersection point. There are three ways of doing it, which we discussed in the class (it is not included in the notes though)
(1) Think of the easiest scenario: A student, Yash Patel came up with the three axis as three lines.
(2) Another simple scenario which I often use is first define the intersection point and then put the (x,y) value in LHS of any equation to get the right hand side. This was used by another student Rajan Hansora, to create a non trivial set of intersecting lines.
(3) One more method that works is to create the third line by taking the linear combination of the first two. This is interesting because of its connection with the matrix row operations.
Even more interestingly not all the three methods given above directly get translated when one wants to discuss intersection of three planes.