115apracticeexam1 - Practice Hour Exam #1 Math 115A Section...

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Unformatted text preview: Practice Hour Exam #1 Math 115A Section 1 NAME: SCORES: 1. / 20 2. / 20 3. / 10 4. / 10 5. / 20 6. / 20 Total: / 100 Problem 1 (20 points - 5 points each) (a) State what it means for a subset S of a vector space V to be linearly independent . (b) Define the dimension of a finite-dimensional vector space. (c) Suppose T : V W is a linear transformation. Define the null space of T . (d) Suppose T : V W is a linear transformation. Define the rank of T . Problem 2 (20 points - 4 points each) For each of the following statements, determine if they are true or false. If they are true, prove them. If they are false, provide a counterexample . (a) dim( P n ( F )) = n . (b) 3 distinct vectors in R 4 must be linearly independent. (c) 3 distinct vectors in R 2 must be linearly dependent. (d) If dim( V ) = n and dim( W ) = m and and are ordered bases for V and W respectively, then [ T ] is an m n-matrix....
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This note was uploaded on 10/08/2011 for the course MATH 115A 262398211 taught by Professor Fuckhead during the Fall '10 term at UCLA.

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115apracticeexam1 - Practice Hour Exam #1 Math 115A Section...

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