HW3Math211S11

HW3Math211S11 - explicitly demonstrates that the set does...

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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
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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...
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