HW3Math211S11

# HW3Math211S11 - explicitly demonstrates that the set does...

This preview shows page 1. Sign up to view the full content.

Math 211: Linear Algebra Homework 3 Due February 25 Part I Read Section 3.2, then ﬁnish reading Section 1.3 in Leon, and do the following problems: (1) 3.2: 11d, 11e, 12b, 12c, 13a, 13b, 15, 16a, 16b Note: These problems will all involve some type of calculation. Be sure to verbally set up the calculation so that it is clear what you are doing and why, and then explain why your conclusion follows by referring back to the deﬁnition of span or spanning set. Be sure to provide complete justiﬁcation in grammatically correct English sentences for both Part I and Part II. Please remember to write Part II on a separate paper than Part I. Part II (1) The following problems ask you to determine whether these sets are subspaces of the corresponding vector space. If yes, prove that the set is a subspace by verifying that they satisfy the deﬁnition of a subspace. If no, provide a concrete counterexample which
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: explicitly demonstrates that the set does not satisfy the deﬁnition of a subspace. 3.2: 1b, 1c, 2a, 2c, 3d, 3f, 5b, 5c, 6d, 6e (2) 3.2.20. Prove the statement for a generic vector space W by verifying that U ∩ V satisﬁes the deﬁnition of a subspace. (3) 3.2.22. Prove the statement for a generic vector space W by verifying that U + V satisﬁes the deﬁnition of a subspace. (4) 3.2.21. Here, “explain” means that if the answer is yes always, prove it. If the answer is not necessarily, provide an explicit example proving that the statement may be false. (5) 3.2.14. Here, “explain” means that if the answer is yes always, prove it. If the answer is not necessarily, provide an explicit example proving that the statement may be false. 1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online