Question

6 Let y = and u Write y as the sum of two orthogonal vectors, one in Span (u) and one orthogonal to u. 5 7 y=y+z=( (Type an integer or simplified fraction for each matrix element. List the terms in the same order as they appear in the original list.)

Answer 1

a tet ZE be the vector which is b to u = () 6 -7 Then their dot 0 on this gonal product should be Lero. i.e, Ziu zou = (on or we can say Yu- Tu :) => 60-76=0. a. => 60 = 76 76.; iid, b= 7 tot t Then Z *)= (-)-a (7) & Thus the set of vectors orthogonal to u is spanned by n (10) 6 imbers tet ceR (set of realnu 13) then cuac +7 belongs to span{u} . we have to write. y=cutz i.es (3) = 4(4)+10 6.c.ta 5 - 70 + 6a

Thus we get 6C +a = 3 --76 +60 = 5 solving these two equations we get a = 21, 2= -1/5 -615 Thus we get cu= () in Span{u} 7/5 and RYS z = a orthogenal to u. = 6 7 185 2.1 and 2 - y- 5 (3)= 0) 5 + + 6 7 / 18 5