Let V be a real vector space with basis v₁, V2. Define 5 - [₁ 2]. Assuming that this makes V, into an inner product space, find an orthonormal basis w₁, W₂ with respect to this inner product in terms of v₁, V₂. v₁ • Vj = aij, where A = (aij) = Select one: O w₁ = (√5v₁ + √2v₂)/√√7, w₂ = (—v₁ − v₂)/√2 O The associated quadratic form q(v) = v.v for the stated dot product is not in fact positive definite, hence there is no orthonormal basis in this case. O w₁ = (v₁ + 2v2)/√√/5, W₂ = (v₁ — v₂)/√2 O w₁ = v₁/√5, W₂ = (v₁ - 5v₂)/√/45 O None of the others apply
Let V be a real vector space with basis v₁, V2. Define 5 - [₁ 2]. Assuming that this makes V, into an inner product space, find an orthonormal basis w₁, W₂ with respect to this inner product in terms of v₁, V₂. v₁ • Vj = aij, where A = (aij) = Select one: O w₁ = (√5v₁ + √2v₂)/√√7, w₂ = (—v₁ − v₂)/√2 O The associated quadratic form q(v) = v.v for the stated dot product is not in fact positive definite, hence there is no orthonormal basis in this case. O w₁ = (v₁ + 2v2)/√√/5, W₂ = (v₁ — v₂)/√2 O w₁ = v₁/√5, W₂ = (v₁ - 5v₂)/√/45 O None of the others apply
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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![Let V be a real vector space with basis v₁, v2. Define
5
- [₁ 2].
Assuming that this makes V, into an inner product space, find an orthonormal basis w₁, W₂ with respect to this inner product in terms of v₁, v₂.
v₁ Vj = aij, where A = (aij) =
Select one:
O w₁ = (√5v₁ + √2v₂)/√√7, w₂ = (v₁ − v₂)/√2
O
The associated quadratic form q(v) = v . v for the stated dot product is not in fact positive definite, hence there is no orthonormal basis in this case.
O
w₁ = (v₁ + 2v2)/√√/5, w₂ = (v₁ − v₂)/√2
O
w₁ = v₁/√5, W₂ = (v₁ - 5v₂)/√/45
O
None of the others apply](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0de9773e-39c1-4df6-a7d6-864501c7f552%2F1b9aaa63-851e-4983-a827-b4e46f5a6875%2Fbtcha2i_processed.png&w=3840&q=75)
Transcribed Image Text:Let V be a real vector space with basis v₁, v2. Define
5
- [₁ 2].
Assuming that this makes V, into an inner product space, find an orthonormal basis w₁, W₂ with respect to this inner product in terms of v₁, v₂.
v₁ Vj = aij, where A = (aij) =
Select one:
O w₁ = (√5v₁ + √2v₂)/√√7, w₂ = (v₁ − v₂)/√2
O
The associated quadratic form q(v) = v . v for the stated dot product is not in fact positive definite, hence there is no orthonormal basis in this case.
O
w₁ = (v₁ + 2v2)/√√/5, w₂ = (v₁ − v₂)/√2
O
w₁ = v₁/√5, W₂ = (v₁ - 5v₂)/√/45
O
None of the others apply
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