12.747 Problem Set #1

Instructions: Download all your files (by shift clicking on the highlighted file names) before starting MATLAB. Write an m-file to reproduce your analysis and e-mail the m-file to the Instructors.
  1. E-mail to David Glover and Andrea Burke your name, your MIT phone number and/or your WHOI extension, your MIT and/or your WHOI office location, department you are affiliated with, mail-stop, and most importantly your e-mail address. (Sorry, no grade credit for this problem).
  2. Download the data matrix A.dat and the column vector b.dat (remember to press shift when you click on them, and to put them in the same directory that you use MATLAB in. Now load them into MATLAB using the command "load A.dat" and "load b.dat". (Make sure you are in the same directory as the files!).
    1. Now solve the equation set designated by Ax=b. This is a set of 7 equations with 7 unknowns. List the values of "x".
    2. What is the rank and determinant of A?
    3. List the singular values for A.
  3. Download A1.dat and b1.dat. Load them into MATLAB. Then, do the following:
    1. What is the rank and determinant of A1?
    2. What happens when you solve A1*x=b1 directly?
    3. Do a singular value decomposition, compute the inverse of A1 by zeroing the singular values and solve for x.