M-221 Midterm: MATH 221 Montana State Exam1Summer14

Show that if w, v, u epsilon R^n such that, u notequalto 0, and w = v - uv/||u||^2 u, then the vector w is orthogonal to u.

Exercise 4. Let (N, v) be defined by N - 11,2,3,4) and v1,2)v(2,3])-v(13,4)(4)1, v(N)-2, and v(S) 0 otherwise. 1. Determine C(N,v) 2. Let a E R and let (N, u) be the game that may differ from (N, v) only inasmuch as y®(N)-a. Describe the set of all ? such that C(X,y®) 0. 3. Show that (N,v) is transitive, that is, for all i, j E N there exists a permutation ? of N with r(i)-1 and u(r(S))-U(S) for all S N.