Find bases for the following subspaces of F5: and W₁ = {(a1, 02, 03, 04, 05) € F5: α₁ - 03 - α4 = 0} W₂ = {(a1, a2, a3, a4, a5) € F5 : a2 = a3 = a4 and a₁ + a5 = 0}. What are the dimensions of W₁ and W₂?
Find bases for the following subspaces of F5: and W₁ = {(a1, 02, 03, 04, 05) € F5: α₁ - 03 - α4 = 0} W₂ = {(a1, a2, a3, a4, a5) € F5 : a2 = a3 = a4 and a₁ + a5 = 0}. What are the dimensions of W₁ and W₂?
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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Transcribed Image Text:14. Find bases for the following subspaces of F5:
and
W₂
-
W₁ = {(a1, a2, a3, a4, a5) F5 a₁ - a3 a4=0}
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{(a1, a2, a3, a4, a5) € F5 : a2 = a3 = a4 and a₁ + a5 = 0}.
What are the dimensions of W₁ and W₂?
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