HW2Math211S11

# HW2Math211S11 - every step, be sure to cite any properties...

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Math 211: Linear Algebra Homework 2 Due by midnight on Thursday, February 17 * Part I Read Section 1.3 pages 27-30 in Leon, and do the following problems: (1) 1.3: 1a, 1b, 1c, 1d 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 Read Section 3.1 in Leon twice , and do the following problems in the suggested order: (1) 3.1.3. Prove that C is a vector space by verifying that axioms C1 - C2 and A1 - A8 hold with the given operations of addition and scalar multiplication of complex numbers. (2) 3.1.15. Prove that S is a vector space by verifying that axioms C1 - C2 and A1 - A8 hold with the given operations of addition and scalar multiplication of sequences of real numbers. At every step, be sure to cite any properties of the real numbers that you are using. (3) 3.1.5. Prove that C [ a,b ] is a vector space by verifying that axioms C1 - C2 and A1 - A8 hold with the given operations of addition and scalar multiplication of functions. At
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Unformatted text preview: every step, be sure to cite any properties of (continuous) functions that you are using. (4) 3.1.10. Prove that this set is not a vector space by explicitly providing a counterexample which demonstrates that at least one of the axioms fails to hold. (5) 3.1.7. Prove using the vector space axioms that any vector which satisﬁes the deﬁning property of the zero vector must actually be the zero vector itself. At every step, be sure to cite which axiom you are using. (6) 3.1.8. Begin with one side of this equality, and work to the other side of the equality using only the vector space axioms. At every step, be sure to cite which axiom you are using. (7) 3.1.9a. Begin with one side of this equality, and work to the other side of the equality using only the vector space axioms. At every step, be sure to cite which axiom you are using. * Two envelopes will be outside of my oﬃce door if you turn the problem set in after 6PM. 1...
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## This document was uploaded on 06/10/2011.

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