Suppose that S₁ and S₂ are nonzero subspaces, with S₁ contained inside S₂, and suppose that dim(S₂) = 3. (a) What are the possible dimensions of S₁ ? ? - (b) If S₁ S₂ then what are the possible dimensions of S₁ ? ?
Suppose that S₁ and S₂ are nonzero subspaces, with S₁ contained inside S₂, and suppose that dim(S₂) = 3. (a) What are the possible dimensions of S₁ ? ? - (b) If S₁ S₂ then what are the possible dimensions of S₁ ? ?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 10EQ
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![Suppose that S₁ and S₂ are nonzero subspaces, with S₁ contained inside S₂, and suppose that dim(S₂) = 3.
(a) What are the possible dimensions of S₁ ? ?
+
(b) If S₁ S₂ then what are the possible dimensions of S₁ ? ?
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35bc7cfb-e38c-45d6-8cb2-8c987ddfb016%2F9c4d9e0b-0617-4d6d-9886-fec64b95b8ad%2F94qxz2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that S₁ and S₂ are nonzero subspaces, with S₁ contained inside S₂, and suppose that dim(S₂) = 3.
(a) What are the possible dimensions of S₁ ? ?
+
(b) If S₁ S₂ then what are the possible dimensions of S₁ ? ?
+
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