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fall1997-midterm - NAME MAS 3114 MID-TERM EXAM Instructions...

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NAME: MAS 3114 MID-TERM EXAM October 15, 1997 Instructions: Total possible points = 100 + 4 bonus pts. 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. Calculators are not allowed. Set out your work properly. Explain your reasoning clearly and make your answer clear. 1. [11 pts] Determine the value(s) of h such that the matrix 1 h 3 2 8 1 is the augmented matrix of a consistent linear system. 2. [8 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. 3. [4 pts] Complete: Asking whether a vector b is in the Span { v 1 , v 2 , . . . , v p } amounts to asking whether the vector equation ....................................................... = b has a ...................................
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