MATH 415 Study Guide - Final Guide: Orthogonal Complement, Linear Combination, Null Character

• School: University of Illinois
• Department: Mathematics
• Course: MATH 415
• Professor: J Li

Document Summary

Suggested practice exercises: chapter 3. 2: 9, 10, 17, 19. 1 review: v, w rn are orthogonal i v w = vt w = v1w1 + vnwn = 0. This means they are perpendicular, or one of them is zero. If v is a subspace of rn, a vector x is orthogonal to v if it is orthogonal to every vector in v . 1 (cid:21) (cid:20)a a(cid:21) = a + a = 0. In fact, it"s enough to check that x is orthogonal to each vector in a basis for v . If x is orthogonal to v = . Then it will be orthogonal to v . v x = 0. More generally, v is always a subspace. V is the null space of vt = (cid:2)2 1 1(cid:3). Find a matrix a such that v = Then it is orthogonal to all x1 + x3 = 0.