a5 - Be sure to explain your work in the diary file in...

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Math 136 Assignment 5 Due: THURSDAY, Feb 26th Section 3-4 Exercises B3. a), b), c) B4. B6 B10 D3 Section 4-1 Exercises B1. a), d), e) B2. a), b) D4 Section 4-2 Exercises B5. D1. D3. D4. D7. MATLAB question is on the next page.
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Use MATLAB to complete the following question. Use the diary feature to record your work. Include a written conclusion for each part in your diary file as well. When finished, print out your diary file and submit it with the rest of your assignment. Vector Spaces Make use of the MATLAB commands rref , null , and rank to help you solve the problems related to vector spaces below. If you’re not familiar with any of these commands, look them up in MATLAB’s Help section. For questions that involve a set of vectors, enter each vector separately, giving it a name (e.g., s1 , s2 , s3 ) and then construct any required matrices from these vectors (e.g., A = [s1 s2 s3] ). This will make it easier for you to work with the various elements.
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Unformatted text preview: Be sure to explain your work in the diary file in addition to including all MATLAB commands and output. (a) Determine if the set S = ±² 1 2 3 4 5 6 ³ , ²-2 8 4 6 9-1 ³ , ² 4 1-2 0-3 ³ , ² 8-3 2 1 10 ³ , ² 14-5-4-12-9-8 ³ , ² 12 10 12 12 20 18 ³´ forms a basis for M 23 . (b) Determine if p ( x ) =-2-3 x-2 x 2 + 7 x 3 belongs to the span of S = { p 1 ,p 2 ,p 3 ,p 4 ,p 5 } , where p 1 ( x ) = 1 + x-x 2-x 3 p 2 ( x ) =-3-x + 2 x 2 + 4 x 3-x 4 p 3 ( x ) = 5 x + x 2-x 4 p 4 ( x ) =-1 + 3 x 3 p 5 ( x ) = 2-x 2 + 2 x 4 (c) Find a basis for the nullspace of A = 2-i 2 i 6 i 3-5 i 3 1 + i 8 i 8-2 i i-4 + i-7-3 i-i . (d) Determine if the following subset of R 5 is linearly independent: { (0 , 8 , ,-8 , 0) , (-2 , , 1 ,-1 , 3) , (5 ,-4 , 1 , 3 , 2) , (-3 , 7 , ,-1 ,-1) , (0 , , ,-3 , 1) } . 2...
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This note was uploaded on 09/04/2009 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

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a5 - Be sure to explain your work in the diary file in...

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