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9. Let F be a field. Find bases of the following two subspaces of F5 : W₁ = {(a₁, a2, a3, a4, a5) = F5 | a₁ a3 a4 = 0}_and W₂ = {(a₁, A2, A3, A4, A5 ) ≤ F5 | a2 = a3 = a4 and a₁ + a5 = 0} 2 What are the dimensions of W₁ and W₂ ?

9. Let F be a field. Find bases of the following two subspaces of F5 : W₁ = {(a₁, a2, a3, a4, a5) = F5 | a₁ a3 a4 = 0}_and W₂ = {(a₁, A2, A3, A4, A5 ) ≤ F5 | a2 = a3 = a4 and a₁ + a5 = 0} 2 What are the dimensions of W₁ and W₂ ?

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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9. Let F be a field. Find bases of the following two subspaces of F5 : W₁ {(a1, a2, a3, a4, a5) € F5 | α₁ — a3 — a4 = 0} and a1 W₂ = {(α1, A2, A3, A4, A5 ) ≤ F5 | a2 = a3 = a₁ and a₁ + a5 = 0} What are the dimensions of W₁ and W₂ ? =
Transcribed Image Text:9. Let F be a field. Find bases of the following two subspaces of F5 : W₁ {(a1, a2, a3, a4, a5) € F5 | α₁ — a3 — a4 = 0} and a1 W₂ = {(α1, A2, A3, A4, A5 ) ≤ F5 | a2 = a3 = a₁ and a₁ + a5 = 0} What are the dimensions of W₁ and W₂ ? =
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