Let 71, 72, 73 be any vectors in a 3-dimensional space. Determine whether the following statements are true or false. You do not have to justify your answer: span(1, U2, U3) = span(302, U3, U1) span(V1, V2, V3) span(v₁ + √2, V2 - V1, V3) If span(7₁, 7₂) = span(7₁, 73), then 72 and 73 are parallel. If 7 = → →

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let 71, 72, 73 be any vectors in a 3-dimensional space.
Determine whether the following statements are true or false. You do not
have to justify your answer:
span(71, 72, 73) = span(372, 73, 71)
span(V1, V2, V3)
=
span(√₁ + √2, V2 — V1, V3)
If span(7₁, 7₂) = span(7₁, 73), then 72 and 73 are parallel.
If 7₁ is a linear combination of 72 and 73, then span(V1, V2, V3)
span(V2, V3).
If 3 is not a linear combination of 7₁ and 72, then span(71, V2, V3) is
strictly larger than span(√₁, √₂).
Transcribed Image Text:Let 71, 72, 73 be any vectors in a 3-dimensional space. Determine whether the following statements are true or false. You do not have to justify your answer: span(71, 72, 73) = span(372, 73, 71) span(V1, V2, V3) = span(√₁ + √2, V2 — V1, V3) If span(7₁, 7₂) = span(7₁, 73), then 72 and 73 are parallel. If 7₁ is a linear combination of 72 and 73, then span(V1, V2, V3) span(V2, V3). If 3 is not a linear combination of 7₁ and 72, then span(71, V2, V3) is strictly larger than span(√₁, √₂).
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