20fmid1 - Math 20F Test 1 100 points-Notation All scalars...

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Math 20F Test 1 100 points January 28, 2009 --------------------------------------------------------------------------------------------------- Notation: All scalars and matrix entries are in the set R of real numbers. Points: (1) , (2) 12 pts each (3A),(3B),(3C) , (4) 15 pts each (3D) 10 pts (3E) 6 pts Directions: Show all work and justify all answers, except in problems (1) and (2). ----------------------------------------------------------------------------------------------------- (1) Let S = { v 1 , . . . , v n } be a set of n vectors in R m . Complete the following sentences in such a way as to provide precise, explicit definitions: (A) The set S is called linearly dependent if ___________________________. (B) The span of S is defined to be the set ______________________________. ------------------------------------------------------------------------------------------------ (2) Let T : R n a R m be a function (i.e., a transformation). Complete the following sentences in such a way as to provide precise, explicit definitions: (A) T is called onto if _________________________________________________. (B) T is called one-to-one
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