# hw2 - Chapter 3 Review Exercises(page 198 1 2 4 6 7 9 26 29...

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MATH 343:001 (11814) Applied Linear Algebra Fall 2009 Homework 2 Due Wednesday, October 14 Assignment. You must turn in answers to the problems from Chapters 3 and 4 AND the MATLAB questions listed below. Basic Concepts in Chapter 3: inner products for vector spaces, the dot product for R n , angles between vectors, length, projection, orthogonal vectors, orthonormal vectors, orthogonal subspaces, orthogonal complements, least squares problem. Basic Skills from Chapter 3: Find orthogonal or orthonormal bases by Gram-Schmidt, understand orthogonality of the 4 subspaces of a matrix, project vectors onto vectors and onto subspaces, ﬁnd projection matrices. Basic Concepts in Chapter 4: determinant, invertible, singular, Cramer’s Rule, cofactors. Basic Skills from Chapter 4: Find determinant by using row reduction and by expansion along a row, use determinant to test invertibility, solve Ax = b and ﬁnd inverses by Cramers Rule, know properties of the determinant and eﬀects of row operations on the determinant.
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Unformatted text preview: Chapter 3, Review Exercises (page 198): # 1, 2, 4, 6, 7, 9, 26, 29, 30 Chapter 4, Review Exercises (page 230): # 1, 2, 3, 13 MATLAB PROBLEMS. (1) Use the template bestline.m from the course website to ﬁnd the equation of the best-ﬁt line (in the least squares sense) to the data in the table below. (Atmospheric CO2 values (ppmv) derived from in situ air samples collected at Mauna Loa, Hawaii, USA. Source: R. F. Keeling, S. C. Piper, A. F. Bollenbacher and S. J. Walker, Carbon Dioxide Research Group, Scripps Institution of Oceanography) Atmospheric (CO 2 ), Mauna Loa 1960 1970 1980 1990 2000 2008 316.91 325.68 338.69 354.19 369.48 385.34 Turn in the following: (a) The normal equations (b) The equation of the line (c) A plot of the data together with the best ﬁt line (2) Review Exercise 4.17 from page 231 in the textbook. Gerardo Laﬀerriere, October 6, 2009 1...
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