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summer2004-midterm

# summer2004-midterm - NAME CODEWORD MAS 3114 MID-TERM EXAM...

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NAME: CODEWORD: MAS 3114 MID-TERM EXAM May 28, 2004 Instructions: Total possible points = 87. In this test boldface is used to indicate a vector; eg. v is a vector but x is a scalar. In your work distinguish between vectors and scalars by underlining vectors; eg. v is a vector but x is a scalar. Show all necessary working. Only scientific calculators are allowed. Set out your work properly. Explain your reasoning clearly and make your answer clear. 1. [4 pts] Complete the following. DEFINITION . If v 1 , v 2 , . . . , v p are in R n , then the set of ....................................... ........................... of v 1 , v 2 , . . . , v p is denoted by Span { v 1 , v 2 , . . . , v p } and is called the subset of R n ......................... (or generated ) by v 1 , v 2 , . . . , v k . That is, the Span { v 1 , v 2 , . . . , v p } is the collection of all vectors that can be written in the form ......................................................................... with .................................... scalars. 2. [6 + 2 = 8 pts] Let A = 1 - 1 7 1 - 2 4 1 3 1 and b = 8 3 10 . Denote the columns of A by a 1 , a 2 , a 3 (a) Determine whether b is in Span { a 1 , a 2 , a 3 } .

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summer2004-midterm - NAME CODEWORD MAS 3114 MID-TERM EXAM...

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