For the vectors u = (3, − 1) and v = (3, − 1), express u as the sum u=p+n, where p is parallel to v and n is orthogonalto v....u=p+n= + (0,0)(Type integers or simplified fractions. List the terms in the same order as they appear in the original list.)

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Answered: For the vectors u = (3,-1) and v=…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Assume v1 = [3,-2] and v2 = [-1,4]. Find the sum and difference of vectors v1 and v2. v1 + v2 = [Answer,Answer] v1 − v2 = [Answer,Answer]
a. Write the vector (8, 5, 30) as a linear combination of a₁ = (4, -4,1), d₂ = (4, -5, 5) and d3 = (0, -4,-4). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ +52 + 6ả3, which would be entered as 4a1 + 5a2 + 6a3. (8,5, 30) = b. Represent the vector (8,5,30) in terms of the ordered basis B = {(4,-4, 1), (4, −5, 5), (0, -4,-4)}. Your answer should be a vector of the general form . [(8, 5, 30)] B =
a. Write the vector (-4,-8, 6) as a linear combination of a₁ (1, -3, -2), a₂ = (-5,–2,5) and ẩ3 = (−1,2,3). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ + 5ả₂ + 6ẩ3, which would be entered as 4a1 + 5a2 + 6a3. (-4,-8, 6) = -3a1+a2+2a3 b. Represent the vector (-4,-8,6) in terms of the ordered basis = {(1, −3,−2), (-5, -2,5),(-1,2,3)}. Your answer should be a vector of the general form . [(-4,-8,6)] =

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For the vectors u = (3,-1) and v= (3,-1), express u as the sum u=p+n, where p is parallel to v and n is orthogonal to v. u=p+n=+0.0) (Type integers or simplified fractions. List the terms in the same order as they appear in the original list.)