# 14-240/Homework Assignment 6

This assignment is due at the tutorials on Tuesday November 4 or at the appropriate mailboxes at the Math Aid Centre, SS 1071, by Thursday November 6 at 5PM. Here and everywhere, neatness counts!! You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong.

Task 1. Read sections 2.1 through 2.3 in our textbook. Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, preread sections 2.4 and 2.5, just to get a feel for the future.

Task 2. Solve problems 20, 21, 24, 25, 26, and 27 on pages 76-77 and problems 1, 5a, 5b, 5c-g, 9, 15 and 16 on pages 84-86, but submit only your solutions of the underlined problems.

Hint for Problem 16 on Page 86. Start with the same bases as in the proof of rank-nullity, add just a bit, and what is the resulting matrix?

Just for fun. Do a web search for the words "OpenGL" and "matrix" (or "matrices") and find out why graphics accelerators in PCs and game consoles do ${\displaystyle 4\times 4}$ (!) matrix multiplications in hardware. (The full explanation is quite involved; perhaps you should just aim to get a taste of it).

A famed creature that owes its mobility to 4x4 matrices.
 Dror's notes above / Students' notes below