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a6 - Bases and Coordinates(a Check that the vectors in S =...

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Math 136 Assignment 6 Due: Wednesday, Mar 4th Section 4-3 Exercises B1. a), c) B2. B5. D2. Section 4-4 Exercises B2. B3. B5. D4. D6. MATLAB question is on the next page.
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Use MATLAB to complete the following questions. 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. 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.
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Unformatted text preview: Bases and Coordinates (a) Check that the vectors in S = ±² 3 1-1 3-1 1 ³ , ² 2 6 0-5 1 1 ³ , ² 0 4 2-2 3 ³ , ² 6 5 4 3 2 1 ³ , ²-8 7 8-7 7 8 ³ , ² 0 6 1 7 7 9 ³´ are linearly independent (and therefore form a basis for M (2 , 3)) and then find the coordinates of M = ² 11 14 9 11 9 9 ³ with respect to this basis. (b) Extend the linearly independent set S = { (2 ,-1 , 2 , 4 , 1 , ,-1) , (2 , ,-2 ,-1 , ,-2 , 2) , (-7 , 8 , ,-5 ,-2 , 3 ,-1) , (1 ,-1 , 3 , 5 , 1 , 1 ,-2) } to form a basis for R 7 . 2...
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