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Author Question: Let = F1dydz - F2dxdz+ F3 dxdy 2(R3) and let u= a1 i+ a2 j+ a3 k and v = b1 i+ b2 j+ b3 k be ... (Read 95 times)

segrsyd

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Question 1

Let  Λ3(Rn) be the vector space of all 3-forms on Rn and Λ5(Rn) be the vector space of all 5-forms on Rn. If  Λ3(Rn)  and Λ5(Rn) have the same dimension, find n.
◦ 4
◦ 8 or -1
◦ 15
◦ 2
◦ 8

Question 2

Let η =  F1dy∧dz - F2dx∧dz+ F3 dx∧dy ∈Λ2(R3) and let  u= a1 i+ a2 j+ a3 k  and v = b1 i+ b2 j+ b3 k  
be vectors in R3. If η is identified by the vector  w= F1 i+ F2 j+ F3 k  then  η (u, v) is equal to
w ∙ (v × u)
w × (u × v)
w ∙ (u + v)
w ∙ (u × v)
w ∙ (v - u)


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Marked as best answer by segrsyd on May 27, 2021

Jane

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segrsyd

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Reply 2 on: May 27, 2021
Excellent


Dinolord

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Reply 3 on: Yesterday
Wow, this really help

 

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