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fall1994-final - MAS 3114 Final Exam Instructions There are...

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MAS 3114 Final Exam December 16, 1994 Instructions: There are 13 problems giving a total of 210 points (this includes 10 bonus points). Answer all these questions. 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. Answer 4(i), (ii) and part of 13(iii) on the test paper. Answer the remainder on your own paper. Write on ONE side of your paper. Leave blank. 1. 2. 3. 4. 5. 6. 10. 7. 11. 8. 12. 9. 13. [1 point] Name: [1 point] Did you write on ONE side of your paper ? 1
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2 1. [4 + 10 = 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 2 - 1 - 2 , v 2 = 1 0 2 0 , v 3 = 3 2 3 - 2 . Determine if v 3 is in the Span { v 1 , v 2 } . 2. [4 + 18 = 22 points] (i) Define what it means for a set { v 1 , v 2 , . . . , v k } of vectors in R n to be linearly independent .
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