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Let {V₁,..., Vk} be an orthogonal set in R". Which of the following are true? Select one or more: ✔ The rank of the n × k matrix with column vectors {V₁, . . . , Vk} is k □ d(vi, Vj) = 1 for every i ‡ j The rank of the n x k matrix with column vectors {V₁,..., Vk} is n If {V₁,..., Vk} is orthonormal, then || Σ_₁ v₂||² = k 0 || Σh_₁ vi||² = Σh_₁ ||vi||²|

Let {V₁,..., Vk} be an orthogonal set in R". Which of the following are true? Select one or more: ✔ The rank of the n × k matrix with column vectors {V₁, . . . , Vk} is k □ d(vi, Vj) = 1 for every i ‡ j The rank of the n x k matrix with column vectors {V₁,..., Vk} is n If {V₁,..., Vk} is orthonormal, then || Σ_₁ v₂||² = k 0 || Σh_₁ vi||² = Σh_₁ ||vi||²|

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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Let {V₁, . . . , Vk} be an orthogonal set in R”. Which of the following are true? Select one or more: ✔ The rank of the n x k matrix with column vectors {V₁, ..., Vk} is k □ d(vi, Vj) The rank of the n x k matrix with column vectors {v₁, ..., vk} is n If {V₁,..., V} is orthonormal, then || ₁ v₁||² = k Ο ||Σ= || = Σ=1||v||2 - 1 for every i + j i=1
Transcribed Image Text:Let {V₁, . . . , Vk} be an orthogonal set in R”. Which of the following are true? Select one or more: ✔ The rank of the n x k matrix with column vectors {V₁, ..., Vk} is k □ d(vi, Vj) The rank of the n x k matrix with column vectors {v₁, ..., vk} is n If {V₁,..., V} is orthonormal, then || ₁ v₁||² = k Ο ||Σ= || = Σ=1||v||2 - 1 for every i + j i=1
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