MAT310 F04 - Problem Points Scores 1 2 3 4 5 6 12 10 10 12...

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Problem 1 2 3 4 5 Bonus: Total: Points 6 12 10 10 12 10 50+10 Scores Mat 310 – Linear Algebra – Fall 2004 Name: Id. #: Lecture #: Test 2 (November 05 / 60 minutes) There are 5 problems worth 50 points total and a bonus problem worth up to 10 points. Show all work. Always indicate carefully what you are doing in each step; otherwise it may not be possible to give you appropriate partial credit. 1. [6 points] Let W 1 and W 2 be linear subspaces of a vector space V such that W 1 + W 2 = V and W 1 W 2 = { 0 } . Prove that for each vector α V there are unique vectors α 1 W 1 and α 2 W 2 such that α = α 1 + α 2 .
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2. [12 points] Consider the vectors in R 4 defined by α 1 = ( - 1 , 0 , 1 , 2) , α 2 = (3 , 4 , - 2 , 5) , α 3 = (1 , 4 , 0 , 9) . (a) [8 points] What is the dimension of the subspace W of R 4 spanned by the three given vectors? Find a basis for W and extend it to a basis B of R 4 . (b)
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This note was uploaded on 09/21/2010 for the course MAT 310 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.

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MAT310 F04 - Problem Points Scores 1 2 3 4 5 6 12 10 10 12...

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