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Unformatted text preview: Math 136 Sample Term Test 2 # 1 NOTES:  In addition to these questions you should also do questions 4d, 5, 6 from sample term test 1 # 1. Also, our test covers change of coordinates. 1. Short Answer Problems a) What is the definition of the row space and column space of a matrix A . b) What is the definition of a subspace. c) What is the definition of a basis. d) Let B = 1 2 1 ,  1 2 , 1 1 1 . If [ ~v ] B = 1 1 1 what is ~v ? e) Let V be a vector space and ~v ∈ V . Prove that ( 1) ~v is the additive inverse of ~v . 2. Let β = { 1 + x 2 , 1 + x + x 2 , 1 + 2 x + 2 x 2 } . a) Show that β is a basis for P 2 . b) Find the β coordinates of the standard basis vectors of P 2 . 3. Determine, with proof, which of the following are subspaces of the given vector space. a) S = { ( x 1 ,x 2 ,x 3 ,x 4 ) ∈ R 4 2 x 1 5 x 4 = 0 and 3 x 2 2 x 4 = 0 } of R 4 ....
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This note was uploaded on 11/25/2010 for the course MATH 136 taught by Professor All during the Spring '08 term at Waterloo.
 Spring '08
 All
 Linear Algebra, Algebra, Addition

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