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AM025b-sample-test3

AM025b-sample-test3 - THE UNIVERSITY OF WESTERN ONTARIO...

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Unformatted text preview: THE UNIVERSITY OF WESTERN ONTARIO DEPARTMENT OF APPLIED MATHEMATICS Applied Mathematics O25a Third Tutorial Test, November 22, 2007 Time: 60 minutes The test is closed book! You are allowed to use only simple calculators. Section 002, Professor Kiriushcheva Name Student Number Show all steps of your calculations. 1. (10 m 2 1 km arias) Use the Gram-Schmidt process to convert the given basis 0 M OMH } into an orthonormal basis. - 2. (10 marks) Find the leastsquares straight line that fits the following data points (—1,——2), (0,1), and (1,5). 3. (20 marks) 1 ——1 2 —1 1 4 —3 ——1 1 *2 3 —-2 —3 2 —3 6 —5 3 —1 0 3.) Find the bases for the fundamental subsPaces of A: row space Row(A), column space Col(A), nullspaces N ull(A) and Null (AT). LetA= b) Find the rank and nullity of A. c) Verify the Rank-Nullity Theorem (Dimension Theorem) for A. d) Verify that Null(A) = (Row(A))i and Null (AT) = (calmni. ...
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