Consider a finite dimensional vector space V with S = Select all the correct options. If S is a linearly dependent set of vectors, then S can never be orthogonal. If S is an orthonormal set of vectors, then S must be an orthonormal basis of V. If EV is orthogonal to each v S, then wis orthogonal to span (S). Tspan(S) (7) € V, then must be orthogonal to span (S). 0000 = {ví, v₂, ... vk } ≤ V \ {0}.\ . Which of the following must necessarily be true? If w = for some

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Consider a finite dimensional vector space V with S = {₁, 2, ... vk } ≤ V \ {0}. . Which of the following must necessarily be true?
Select all the correct options.
If S is a linearly dependent set of vectors, then S can never be orthogonal.
If S is an orthonormal set of vectors, then S must be an orthonormal basis of V.
If w€ V is orthogonal to each v € S, then wis orthogonal to span (S).
Tspan(S) (7)
If w
=
for some
V
EV, then must be orthogonal to span(S).
Transcribed Image Text:Consider a finite dimensional vector space V with S = {₁, 2, ... vk } ≤ V \ {0}. . Which of the following must necessarily be true? Select all the correct options. If S is a linearly dependent set of vectors, then S can never be orthogonal. If S is an orthonormal set of vectors, then S must be an orthonormal basis of V. If w€ V is orthogonal to each v € S, then wis orthogonal to span (S). Tspan(S) (7) If w = for some V EV, then must be orthogonal to span(S).
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