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# HW2 - COT4501 Spring 2012 Homework II This assignment has...

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COT4501 Spring 2012 Homework II This assignment has eight problems and they are equally weighted. The assignment is due in class on Tuesday, February 14, 2012. There are six regular problems and two computer problems (using MATLAB). For the computer problems, turn in your results (e.g., graphs, plots, simple analysis and so on) and also a printout of your (MATLAB) code. Problem 1 Provide short answers to the following questions: True or false: At the solution to a linear least squares problem Ax b , the residual vector r = b - Ax is orthogonal to span ( A ) . True or false: In solving a linear least squares problem Ax b , if the vector b lies in span ( A ) , then the residual is 0 . In a linear least squares problem Ax b , where A is an m × n matrix, if rank ( A ) < n , then which of the following situation are possible? 1. There is no solution. 2. There is a unique solution. 3. There is a solution, but it is not unique. in Solving an overdetermined least squares problem Ax b ,which would be more serious difficulty: that the rows of A are linearly dependent, or that the columns of A are linear dependent? Explain.

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