Question

Find a basis for the orthognonal complement of U=span Lona i Number of Vectors: 1 Basis for Uł:

Answer 1

Griveno u = spama 3 we have to find basis for the orthogonal complement of u. i. e. for ut ut = { x = (a, b, c, d) EIRY : x = 0 tur 3 le x.up = 0 5a + 2b + 20+ 20 = 0 0 IX.uz = 0 5a + ab + 2c +3d 20 - a. Ug = 0 Sa+26+2c-d=0 - .: O. @ $3)) (5 2 2 2 1 5 2 2 3 15 2 2 R₂ R2 - R1, R₂ RB-R, 5 2 2 2 1 0 0 0 1 0 0 0 - 3 Goog 1 [:]

5atabt act 2d = 0 al- o -3d=0 > BIS d=0 -2b - 20 C o as d=0 reduces to 5a + 2b +2c=0 - a=-26 - 20 = 65-215 7 cc-2157 - SO dhoo ono Basis for ut is = { 1 } ] . 1 - 3 / 3 ο . Nole: we have that basis taken to get a common so simpler form.