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Suppose that S1 and S2 are nonzero subspaces, with S₁ contained inside S2, and suppose that dim(S2) = 4 ? ✓ 1. What are the possible dimensions of S₁? ? 2. If S1 S2, then what are the possible dimensions of S1 ? Suppose U and V are subspaces of a vector space W. If dim(U) = 10, dim(V) = 10, and dim(U + V) = 17 then dim(Un V)

Suppose that S1 and S2 are nonzero subspaces, with S₁ contained inside S2, and suppose that dim(S2) = 4 ? ✓ 1. What are the possible dimensions of S₁? ? 2. If S1 S2, then what are the possible dimensions of S1 ? Suppose U and V are subspaces of a vector space W. If dim(U) = 10, dim(V) = 10, and dim(U + V) = 17 then dim(Un V)

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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Suppose that S1 and S2 are nonzero subspaces, with S₁ contained inside S2, and suppose that dim(S2) = 4 ? ✓ 1. What are the possible dimensions of S₁? ? 2. If S1 S2, then what are the possible dimensions of S1 ?
Transcribed Image Text:Suppose that S1 and S2 are nonzero subspaces, with S₁ contained inside S2, and suppose that dim(S2) = 4 ? ✓ 1. What are the possible dimensions of S₁? ? 2. If S1 S2, then what are the possible dimensions of S1 ?
Suppose U and V are subspaces of a vector space W. If dim(U) = 10, dim(V) = 10, and dim(U + V) = 17 then dim(Un V)
Transcribed Image Text:Suppose U and V are subspaces of a vector space W. If dim(U) = 10, dim(V) = 10, and dim(U + V) = 17 then dim(Un V)
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