#11 6.3.19 A Question Help 0 Let uy = 2 -2, and uz = 0 . Note that u, and uz are orthogonal but that uz is not orthogonal to u, oruz. It can be shown that uz is not in the subspace 2 W spanned by U, and up. Use this fact to construct a nonzero vector v in R3 that is orthogonal tou, and uz. A nonzero vector in R3 that is orthogonal tou, and uz is v=
Note that u, and u are orthogonal. It can be shown that ug is not in the subspace W spanned by u, and up. Use this to construct a nonzero vector v in R that is orthogonal tou, and un The nonzero vector v= | is orthogonal to u, and up.
Find the best approximation to z by vectors of the form C7 V + c2V2. 3 1 3 -1 -6 1 z = V2 4 0 -3 3 1 The best approximation to z is . (Simplify your answer.) - 15 - 8 8 - 1 Let y = , and v2 Find the distance from y to the subspace W of R* spanned by V, and vą, given 1 0 1 - 15 3 3 - 13 09 that...
(1 point) Given v = find the coordinates for v in the subspace W spanned by U = , U2 = 0 and Ug = Note that uy, U, and Uz are orthogonal. v= u+ U2+ 213
(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...
(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...
5/9/2019 the closest point to y in the subspace W spanned by u, and u Let W be the subspace spanned by 11. and u2. Write y as the sum of a vector in W and a vector orthogonal to w u, 12 13)- 12 25 3 5 6-5 | and b = | 4 l. Describe the general solution in parametric Describe all solutions of Ax = b, where A-1-2 -4 7 0 vector form
#5 6.3.8 Let W be the subspace spanned by U, and up. Write y as the sum of a vector in W and a vector orthogonal to W. -1 -2 y = un = 3 2 -1 The sum is y = y +z, where y 8. is in W and z = Doo is orthogonal to W. (Simplify your answers.)
(1 point) Consider the two dimensional subspace U of R* spanned by the set {u1, u2} where [1] u = T 37 -1 1-3] U2 = 3 : The orthogonal complement V = Ut of U ER is the one dimensional subspace of Rº such that every vector ve V is orthogonal to every vector ue U. In other words, u: v=0 for all ue U and ve V. Find the first two components V1 and 12 of the vector...
Show that (u, u2 ub) is an orthogonal basis for R Thon express as a inear of the u's Which of the following cniteria are necessary for a set of vectors to be an orthogonal basis for a subspace W of IR? Select all that apply A. The vectors must span W B. The vectors must all have a length of 1 D C. The distance between any pair of distinct vectors must be constant D. The vectors must form...