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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