(1 point) 1 Let y = , U1 = 1 Compute the distance d from y to the plane in R} spanned by uj and U2 - d = 654.33
2 1 3 4 -2 5 7 -2 9 Problem 9 Let uj = u2 = 13 2 Also let v= 0 5 3 10 -6 0 11 1 1 7 a) (4 pts) Compute prw(v) where W = Span{u1, U2, U3} CR5. b) [4 pts) Compute prw(v) where w+ denotes the orthogonal complement of W in R5. c) [3 pts) Compute the distance between v and W.
#8 6.3.15 6 -3 -2 Let y = u- U2 - 1 Find the distance from y to the plane in R3 spanned by u, and uz: 3 1 -2 The distance is (Type an exact answer, using radicals as needed.)
(1 point) 0 Given v 3 find the linear combination for v in the subspace W spanned by 0 0 3 3 and 114 , u2 = , из- 4 4 Note that ul , u2 , u3 and 14 are orthogonal. u1+ 7 U2 ll4 (1 point) 0 Given v 3 find the linear combination for v in the subspace W spanned by 0 0 3 3 and 114 , u2 = , из- 4 4 Note that ul...
(1 point) -5 -2 -1 -2 2 Let y = Vi = V2 2 4 3 -6 1 -18 Compute the distance d from y to the subspace of R4 spanned by vi and v2. d
(1 point) -3 10 9 Given v = 9 find the coordinates for u in the subspace W spanned by 1 0 3 -3 -1 5 4 U1 = = , U2 = , U3 and 14 -7 1 Note that uj, U2, U3 and 14 are orthogonal. 2 U = U1+ U2+ U3+ 14
(1 point) 1 -2 -2 4 -4 -3 0 4 -4 Let y = Vi = V2 = 3 1 0 Compute the distance d from y to the subspace of R* spanned by Vị and V2 . d =
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29 ( 7 Answer the following questions and give proper explanations. (a) Is {ui, U2, uz} a basis for R3? (b) Is {ui, U2, u4} a basis for R4? (c) Is {ui, U2, U3, U4, u; } a basis for R? (d) Is {ui, U2, U3, u} a basis for Rº?! (e) Are ui, u, and O linearly independent?! Problem 6. (15 points). Let A...
Exercise 3. Let u2= (5) C) V2 = V1 = and E u1, u2},F = {v1,v2} be two ordered bases for R2. Let also 5 (i) Find the coordinate vectors of [x]E and [x\f. (ii) Find the transition matrix S from the basis E to F. (ii) Verify that [x]f = S[r]E Exercise 3. Let u2= (5) C) V2 = V1 = and E u1, u2},F = {v1,v2} be two ordered bases for R2. Let also 5 (i) Find the...
(1 point) Let {uj, u2, u2 ) be an orthonormal basis for an inner product space V. Suppose y = qui + buz + cuz is so that|lvl1 = V116. (v, uz) = 10, and (v. uz) = 4. Find the possible values for a, b, and c. a = CE (1 point) Suppose U1, U2, Uz is an orthogonal set of vectors in Rº. Let w be a vector in Span(v1, 02, 03) such that UjUi = 42, 02.02...