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Unformatted text preview: Math 136 Sample Term Test 2 # 2 NOTES:  In addition to these questions you should also do questions 7, 10 b from sample term test 1 # 2. 1. Short Answer Problems a) Let S = { v 1 ,...,v n } be a nonempty subset of a vector space V . Define the statement S is linearly independent. b) Write the definition of a subspace S of a vector space V . c) Write the definition of the dimension of a vector space V . d) Prove that 0 x = for any x ∈ V . e) Is it true that if a set S with more than one vector is linearly dependent then every vector v ∈ S can be written as a linear combination of the other vectors. Justify your answer. 2. Let β = { x 2 4 x + 4 ,x 2 , 1 } . a) Show that span( β ) = P 2 . b) Let w = x 2 + x + 1. Find the β coordinate vector of w . 3. Determine, with proof, which of the following are subspaces of the given vector space. a) S = { ax 2 + bx + c  b 2 4 ac = 0 } of P 2 ....
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This note was uploaded on 04/30/2010 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.
 Winter '08
 All
 Addition, Vector Space

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