Let W₁ = 1, W₂ =O-√30112bd0I3سار[2]20=0and let W= span & W₁, W₂, Wz?.Lemon ortha na boila) Determine if the set {W₁, W₂, W3 { is linearly independent or dependent.b) Give dim W and dim (W+).C) Find an orthogonal basis for W.

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Answered: Let W₁ = 1, W₂ = √3, W3 = 2 O 0 O 1 0 .…

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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Do the vectors form a basis for R"? Show which conditions, if any, are met, and show which conditions, if any, are not met. Be sure to address all conditions of a basis. a) v1 = (1,3, –2), v2 = (-2,–6,4) b) v1 = (2,1,0,3), v2 = (0,1,5,7), v3 = (0,0,3, –1), v4 = (0,0,0, –4)
8.) find a vector of norm 2 that is orthogonal to the three vectors, u=(2,1,0), v=(-1,- 1,0) and w=(4,0,0) 9.) find scalars a, b and c such that a(2,0,1) +b (1,3,2)+c(1,0,1)=(7,3,4)
Let V be the vector space of functions spanned by B = {bị 2 sin r + 6 cos a, b2 = 3 sin a + 7 cos a} where a + %3D C = {ci = sin a, c2 = of coordinates matrix P ne Z is also a basis for V. Find the change 2 = cos a} where a + C+B Ex: 5 P = C-B The coordinates of a function f(x) relative to the basis B are [f(x)]B Find the coordinates of f(æ) relative to Cand find f(æ). Ex: 5 [f(x)]c = f(x) = Ex: 5 sin z + cos a
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Let W₁ = 1, W₂ = √3, W3 = 2 O 0 O 1 0 . ارے and let W= spon! W₁, W₂, W₂}, a) Determine if the set {W, W₂, Ws { is linearly independent or dependent. b) Give dim Wand dim (W+). C) Find an orthogonal basis for W.