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quiz2 - Linear Algebra Fall 2002 Quiz 2 13:10 PM 14:25...

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Linear Algebra, Fall 2002 Quiz 2 Nov 29 2002, 13:10 PM - 14:25 PM (1) (15 pts) Which of the following are subspaces of R 2 ? Explain. (a) y = x (b) y = x 2 (c) y = 2 x + 1 (2) (20 pts) True of False? Explain. If S and T are subspaces of a vector space V , so is S ∪ T . (3) (20 pts) Find a basis for N ( A ) with A = 1 2 3 - 1 - 2 - 4 6 3 (4) (15 pts) Is 1 + x + x 2 , 1 + x - x 2 , and 1 + x linearly dependent in P 3 ? Explain. (5) (30 pts) (a) What can you say for sure about the linear dependency and the span of
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