MATH 131 Final: MATH 131 UMass Amherst Umass_FinalExam_2014

• School: UMASS-Amherst
• Department: Mathematics
• Course: MATH 131
• Professor: All

Document Summary

Solutions to quiz 4: 8 points apply the gram-schmidt process to the vectors ~v1 = (cid:20)3 and write the result in the form a = q r. 1 + 9 = r22 = k ~w2k. A = q r (cid:2)~v1 ~v1(cid:3) =(cid:2)~u1 ~u2(cid:3) (cid:20)r11 r12 r22(cid:21) (cid:20)3 2. 1 (a) find the matrix of the orthogonal projection onto the line l in r4 spanned by ~v. 0 (b) find the projection of ~w onto the line l. projl( ~w) = a ~w = Let a = a b c d e f g h i . B = (a aa ) = (a ) a (a ) = aa a and this does not equal b, in general. B = (2a + 2a ) = 2a + 2(a ) = 2a + 2a = b. Thus b is symmetric. (c) suppose a is orthogonal.