fall1994-midterm - MAS 3114 Test 1 Instructions There are 8...

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MAS 3114 Test 1 September 28, 1994 Instructions: There are 8 problems giving a total of 100 points. Answer all these questions. There is one bonus problem worth 5 points. 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. Leave blank. 1. 2. 3. 4. 5. 6. 7. 8. 9. [1 point] Name: 1
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2 1. [6 points] Suppose that a system of linear equations has a 3 × 5 augmented matrix whose fifth column is a pivot column. Is the system consistent? Why? 2. [3 + 11 = 14 points] (i) Let v 1 , v 2 , . . . , v p be vectors in R n . Define the set denoted by Span { v 1 , v 2 , . . . , v p } . (ii) Let v 1 = 1 1 4 , v 2 = 1 2 6 , v 3 = 1 - 1 0 . Determine if v 3 is in the Span { v 1 , v 2 } .
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