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a) Consider a set of vectors R=(k, kx, kx, e**) where k is a scalar. i. Find the Wronskian, W(x) for the set. ii. Find the range of k such that the set is linearly independent. b) Find the angle, e between vectors u = (2,5) and v= (1,2) with the Euclidean inner product (u, v) = 3u₂v₁ + 2v₂u₁. State the orthogonality of the vectors. c) Express the vector v = (1,2,5) as a linear combination of v₁ = (1,1,1), V₂ =

a) Consider a set of vectors R=(k, kx, kx, e**) where k is a scalar. i. Find the Wronskian, W(x) for the set. ii. Find the range of k such that the set is linearly independent. b) Find the angle, e between vectors u = (2,5) and v= (1,2) with the Euclidean inner product (u, v) = 3u₂v₁ + 2v₂u₁. State the orthogonality of the vectors. c) Express the vector v = (1,2,5) as a linear combination of v₁ = (1,1,1), V₂ =

Advanced Engineering Mathematics
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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a) Consider a set of vectors R = {k, kx, kx, e**) where k is a scalar. i. Find the Wronskian, W(x) for the set. i. Find the range of k such that the set is linearly independent. b) Find the angle, e between vectors u = (2,5) and v = (1,2) with the Euclidean inner product (u, v) = 3u₂v₁ +2v₂u₁. State the orthogonality of the vectors. c) Express the vector v = (1,2,5) as a (1,2,3) and v3 = (2,-1,1). linear combination of v₁ = (1.1.1). V₂ =
Transcribed Image Text:a) Consider a set of vectors R = {k, kx, kx, e**) where k is a scalar. i. Find the Wronskian, W(x) for the set. i. Find the range of k such that the set is linearly independent. b) Find the angle, e between vectors u = (2,5) and v = (1,2) with the Euclidean inner product (u, v) = 3u₂v₁ +2v₂u₁. State the orthogonality of the vectors. c) Express the vector v = (1,2,5) as a (1,2,3) and v3 = (2,-1,1). linear combination of v₁ = (1.1.1). V₂ =
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