MATH 240 Lecture Notes - Lecture 24: Dot Product, Scalar Multiplication, Novella

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 240
• Professor: Michael Monagan

Document Summary

Math 240 solutions to assignment 6, fall 2018. Please don"t distribute my solutions on course hero or anywhere on the internet. Use the transpose de nition of the inner (dot) product to prove parts (b) and (c) of theorem 1. This means use u v = ut v. (b) (u + v) w = (u + v)t w = (ut + vt )w = ut w + vt w = u w + v w. I used theorem 3(b) and theorem 2(c). (c) (cu) v = (cu)t v = (cut )v = c(ut v) = c(u v) I used theorem 3(c) and theorem 2(d). (cu) v = (cu)t v = (cut )v = ut (cv) = ut (cv) I also asked you to give alternative proofs which just use the de nition for the dot product and de nition for vector addition and scalar multiplication. (b) (c) And (u + v) w = ([u1, .