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# HW6 - Math 3013 Homework Set 6 Problems from 3.1(pgs...

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Math 3013 Homework Set 6 Problems from § 3.1 (pgs. 134-136 of text): 11,16,18 Problems from § 3.2 (pgs. 140-141 of text): 4,8,12,23,25,26 1. (Problems 3.1.11 and 3.1.16 in text). Determine whether the given set is closed under the usual operations of addition and scalar multiplication, and is a (real) vector space. (a) The set of all diagonal n × n matrices. (b) The set P n of all polynomials in x , with real coeﬃcients and of degree less than or equal to n , together with the zero polynomial. 2. (Problem 3.1.18 in text). Determine whether the following statements are true or false. (a) Matrix multiplication is a vector space operation on the set M m × n of m × n matrices. (b) Matrix multiplication is a vector space operation on the set M n × n of square n × n matrices. (c) Multiplication of any vector by the zero scalar always yields the zero vector. (d) Multiplication of a non-zero vector by a non-zero scalar always yields a non-zero vector. (e) No vector is its own additive inverse.

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HW6 - Math 3013 Homework Set 6 Problems from 3.1(pgs...

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