r₁v₁ + 1₂v₂+...+rkvk = 0 a) v₁ = (3,-1,2), v₂ = (5,4,-6) and v3 = (8,3,-4) b) v₁ = (1, -2), v₂ = (-1,3) and v3 = (1,0) c) v₁ = (3,-1,0,2), v₂ = (1, -2,3,0), v3 = (3,0,0,1) and v4 = (4, -3,3,2)

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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Determine whether the set of vectors S = { V₁ , V₂ , ... , Vk } is linearly independent or linearly dependent . If it is a linearly dependent set , find a set of scalers 1₁ , 12 , ... , Tk ( not all zeros ) such that
r₁v₁ + 1₂V₂+...+rkvk = 0
a) v₁ = (3,-1,2), v₂ = (5,4,-6) and v3 = (8,3,-4)
b) v₁ = (1, -2), v₂ = (-1,3) and V3 = (1,0)
c) v₁ = (3,-1,0,2), v₂ = (1, -2,3,0), v3 = (3,0,0,1) and v4 = (4, -3,3,2)
Transcribed Image Text:r₁v₁ + 1₂V₂+...+rkvk = 0 a) v₁ = (3,-1,2), v₂ = (5,4,-6) and v3 = (8,3,-4) b) v₁ = (1, -2), v₂ = (-1,3) and V3 = (1,0) c) v₁ = (3,-1,0,2), v₂ = (1, -2,3,0), v3 = (3,0,0,1) and v4 = (4, -3,3,2)
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