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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 non-empty 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 = { x 2- 4 x + 4 ,x- 2 , 1 } . a) Show that span( ) = P 2 . b) Let w = x 2 + x + 1. Find the 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 6 = 0 } of P 2 ....

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