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HW10Math211S11

# HW10Math211S11 - B a basis for V Prove that the coordinate...

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Math 211: Linear Algebra Homework 10 Due May 13 Part I Read Sections 4.1, 4.2, and 4.3 in Leon, and do the following problems: (1) 4.1: 1ac, 6, 7cd, 9ab, 17bc, 19b, 22 (2) 4.2: 2a, 4c, 5d, 14a (3) 4.3: 2, 4, 5 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) 4.1: 13, 16, 21 (2) Let V be an n -dimensional vector space and
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Unformatted text preview: B a basis for V . Prove that the coordinate mapping v-→ [ v ] B from V to R n is a linear transformation. (*) Bonus: Refer back to problems 21 and 22 in 4.1 for the deﬁnitions of one-to-one and onto linear transformations. If V is an n-dimensional vector space, prove that the coordinate mapping from V to R n is both one-to-one and onto. (3) 4.2: 20 (*) Bonus: 4.2: 19 1...
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