Homework Answers
(1 point) -1 -3 -2 Let y = 3 , U1 = -2 -5 2 U2...
(1 point) -1 -3 -2 Let y = 3 , U1 = -2 -5 2 U2 = -7 -1 16 Compute the distance d from y to the plane in R’ spanned by uj and u2. d=
#8 6.3.15 6 -3 -2 Let y = u- U2 - 1 Find the distance from...
#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.)
2 4 Let y = 5 uz = 2 Find the distance from y to the...
2 4 Let y = 5 uz = 2 Find the distance from y to the plane in R spanned by u, and uz. 3 1 2 The distance is (Type an exact answer, using radicals as needed.)
(1 point) 1 -2 -2 4 -4 -3 0 4 -4 Let y = Vi =...
(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 point) -3 10 9 Given v = 9 find the coordinates for u in the...
(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) Let u4 be a linear combination of {u1, U2, U3}. Select the best statement....
(1 point) Let u4 be a linear combination of {u1, U2, U3}. Select the best statement. O A. We only know that span{u1, U2, U3, u4} span{u1, u2, u3} . B. There is no obvious relationship between span{u1, U2, uz} and span{u1, U2, U3, u4} . C. span{u1, U2, U3} = span{u1, U2, U3, u4} when none of {u1, U2, uz} is a linear combination of the others. D. We only know that span{u1, U2, U3} C span{u1, U2, U3,...
Let uj = [1,1,1]* and u2 = [1,2,2]t be vectors in R3 and V be the...
Let uj = [1,1,1]* and u2 = [1,2,2]t be vectors in R3 and V be the vector space spanned by {u1, U2}. a. 6pt Use Gram-Schmidt orthogonalization to find an orthonormal basis for V. b. 4pt Let w = [1,0,1)+. Find the vector in V that is closest to w.
(1 point) -5 -2 -1 -2 2 Let y = Vi = V2 2 4 3...
(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) Let {uj, u2, u2 ) be an orthonormal basis for an inner product space...
(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...
- 4 -1 -2 1 Let y = V1 = and V2 Find the distance from...
- 4 -1 -2 1 Let y = V1 = and V2 Find the distance from y to the subspace W of R4 spanned by V, and V2, given that the closest 1 -1 0 13 3 -1 -5 point to y in W is y= نيا 9 The distance is (Simplify your answer. Type an exact answer, using radicals as needed.)
(1 point) -1 -3 -2 Let y = 3 , U1 = -2 -5 2 U2 = -7 -1 16 Compute the distance d from y to the plane in R’ spanned by uj and u2. d=
#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.)
2 4 Let y = 5 uz = 2 Find the distance from y to the plane in R spanned by u, and uz. 3 1 2 The distance is (Type an exact answer, using radicals as needed.)
(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 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) Let u4 be a linear combination of {u1, U2, U3}. Select the best statement. O A. We only know that span{u1, U2, U3, u4} span{u1, u2, u3} . B. There is no obvious relationship between span{u1, U2, uz} and span{u1, U2, U3, u4} . C. span{u1, U2, U3} = span{u1, U2, U3, u4} when none of {u1, U2, uz} is a linear combination of the others. D. We only know that span{u1, U2, U3} C span{u1, U2, U3,...
Let uj = [1,1,1]* and u2 = [1,2,2]t be vectors in R3 and V be the vector space spanned by {u1, U2}. a. 6pt Use Gram-Schmidt orthogonalization to find an orthonormal basis for V. b. 4pt Let w = [1,0,1)+. Find the vector in V that is closest to w.
(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) 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...
- 4 -1 -2 1 Let y = V1 = and V2 Find the distance from y to the subspace W of R4 spanned by V, and V2, given that the closest 1 -1 0 13 3 -1 -5 point to y in W is y= نيا 9 The distance is (Simplify your answer. Type an exact answer, using radicals as needed.)
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