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(1 point) -6 -3 Use Theorem 5.5.2 to write the vector v = -4 as linear...
Section 5.5 Orthonormal Sets: Problem 3 Previous Problem Problem List Next Problem (1 point) -5 Use...
Section 5.5 Orthonormal Sets: Problem 3 Previous Problem Problem List Next Problem (1 point) -5 Use Theorem 5.5.2 to write the vector v = -6 10 as linear combination of -1/V19 -3/V10 3/7190 U1 = -3/719 , U2 = 0/V10 and uz = -10/190 -3/V19 1/V10 9/7190 Note that ui, u2 and uz are orthonormal. V = uj+ u2+ U3 Use Parseval's formula to compute ||v||2. ||01|2
(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...
2) Given 3 vectors. 11 | u = 0 | u = -1 L2 a) What...
2) Given 3 vectors. 11 | u = 0 | u = -1 L2 a) What vector space do these vectors belong to? b) Geometrically describe the space spanned by vectors uj and u2. c) Is vector, v, in the subspace spanned by the vectors uj and u2? d) Are all 3 vectors linearly dependent or independent of each other? Explain why or why not. e) If possible, find the linear combination of vectors u; and uz that equals vector...
Write v as a linear combination of ui, uz, and U3, if possible. (If not possible,...
Write v as a linear combination of ui, uz, and U3, if possible. (If not possible, enter IMPOSSIBLE.) v=(4, -22, -9, -10), 41 = (1, -3, 1, 1), u2 = (-1, 3, 2, 3), U3 = (0, -2, -2, -2) U1 + uz + U3
Please show the detail, thank you! (1 point) (a) Let -4 -7 -2 -4 V1 =...
Please show the detail, thank you!
(1 point) (a) Let -4 -7 -2 -4 V1 = and V2 = 1 6 0 2 and let W = span{V1, V2}. Apply the Gram-Schmidt procedure to vi and V2 to find an orthogonal basis {uj, u2 } for W. uj = U2 = -13 2 (b) Consider the vector v = - Find V' E W such that || V – v' || is as small as possible. 15 8 V =...
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1),...
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1), uz = 5(–1,1,1,1). (a) Check that {uj,uz) is an orthonormal set using the dot product on R. (Hence it forms an orthonormal basis for W.) (b) Let w = (-1,1,5,5) EW. Using the formula in the box above, express was a linear combination of u and u. (c) Let v = (-1,1,3,5) = R'. Find the orthogonal projection of v onto W.
(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...
(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...
0 (1 point) Let uz = 4. → U12 = ,113 = 4 Which of the...
0 (1 point) Let uz = 4. → U12 = ,113 = 4 Which of the following are in the span of u1, 12, uz? 6 A. 8 4 :-2 B. 8 1 C. Write the following vector as a linear combination of u1, U2, U3. If it is not possible, leave each entry empty. + () + [:1-03 3
(a) Write the vector aas a linear combination of the set of orthonormal basis vectors 2 marks] (b) Find the orthogonal...
(a) Write the vector aas a linear combination of the set of orthonormal basis vectors 2 marks] (b) Find the orthogonal projection of the vector (1,-3) on the vector v- (-1,5). 2 marks] (c) Using your result for part (b) verify that w = u-prolvu is perpendicular to V. 2 marks]
(a) Write the vector aas a linear combination of the set of orthonormal basis vectors 2 marks] (b) Find the orthogonal projection of the vector (1,-3) on the vector...
4 We can write the vector V = | 3 | in the 2. linear combination...
4 We can write the vector V = | 3 | in the 2. linear combination of basis vectors 4 2. i = 4 12 = -6 6 5 3 = 3 as 4 Select one: 이 A. V = Su + 2 + u3 B. None of these answers 18 2 11 O 0 118 p. V = ful + 2 - ITU3 O E. V = -fu] + 2 - 13
Section 5.5 Orthonormal Sets: Problem 3 Previous Problem Problem List Next Problem (1 point) -5 Use Theorem 5.5.2 to write the vector v = -6 10 as linear combination of -1/V19 -3/V10 3/7190 U1 = -3/719 , U2 = 0/V10 and uz = -10/190 -3/V19 1/V10 9/7190 Note that ui, u2 and uz are orthonormal. V = uj+ u2+ U3 Use Parseval's formula to compute ||v||2. ||01|2
(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...
2) Given 3 vectors. 11 | u = 0 | u = -1 L2 a) What vector space do these vectors belong to? b) Geometrically describe the space spanned by vectors uj and u2. c) Is vector, v, in the subspace spanned by the vectors uj and u2? d) Are all 3 vectors linearly dependent or independent of each other? Explain why or why not. e) If possible, find the linear combination of vectors u; and uz that equals vector...
Write v as a linear combination of ui, uz, and U3, if possible. (If not possible, enter IMPOSSIBLE.) v=(4, -22, -9, -10), 41 = (1, -3, 1, 1), u2 = (-1, 3, 2, 3), U3 = (0, -2, -2, -2) U1 + uz + U3
Please show the detail, thank you!
(1 point) (a) Let -4 -7 -2 -4 V1 = and V2 = 1 6 0 2 and let W = span{V1, V2}. Apply the Gram-Schmidt procedure to vi and V2 to find an orthogonal basis {uj, u2 } for W. uj = U2 = -13 2 (b) Consider the vector v = - Find V' E W such that || V – v' || is as small as possible. 15 8 V =...
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1), uz = 5(–1,1,1,1). (a) Check that {uj,uz) is an orthonormal set using the dot product on R. (Hence it forms an orthonormal basis for W.) (b) Let w = (-1,1,5,5) EW. Using the formula in the box above, express was a linear combination of u and u. (c) Let v = (-1,1,3,5) = R'. Find the orthogonal projection of v onto W.
(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...
0 (1 point) Let uz = 4. → U12 = ,113 = 4 Which of the following are in the span of u1, 12, uz? 6 A. 8 4 :-2 B. 8 1 C. Write the following vector as a linear combination of u1, U2, U3. If it is not possible, leave each entry empty. + () + [:1-03 3
(a) Write the vector aas a linear combination of the set of orthonormal basis vectors 2 marks] (b) Find the orthogonal projection of the vector (1,-3) on the vector v- (-1,5). 2 marks] (c) Using your result for part (b) verify that w = u-prolvu is perpendicular to V. 2 marks]
(a) Write the vector aas a linear combination of the set of orthonormal basis vectors 2 marks] (b) Find the orthogonal projection of the vector (1,-3) on the vector...
4 We can write the vector V = | 3 | in the 2. linear combination of basis vectors 4 2. i = 4 12 = -6 6 5 3 = 3 as 4 Select one: 이 A. V = Su + 2 + u3 B. None of these answers 18 2 11 O 0 118 p. V = ful + 2 - ITU3 O E. V = -fu] + 2 - 13
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