Chapter 1.2, Problem 40EQ

Section 1.3 1. Let u (a) Draw u and v in R2. (b) Use the parallelogram law to add 2u - v to your picture. (c) Calculate 2u - v and verify it coincides with your sketch in part (b). (d) What is Span(u, v}? 2. Consider the set of vectors Va = (a) Describe Span{v1, Va, Va). (b) Is b= 3 in Span(vi, Va, Va)? 3

Let m (1, 2, 3) and n (5, 3,-2). Find the vector projection of m onto n, that is, find proj- m. You do not need to simplify (radicals in denominators are okay).

Compute the orthogonal projection of v= 7 onto the line through 4 2 and the origin.